travelling disturbance definition

The Sun Spot

What Is a TID? It’s a TAD More Complicated Than We Thought

By Miles Hatfield NASA’s Goddard Space Flight Center

About 50 miles up, Earth’s atmosphere undergoes a fundamental change. It starts at the atomic level, affecting only one out of every million atoms (but with about 91 billion crammed in a pinhead-sized pocket of air, that’s plenty). At that height, unfiltered sunlight begins cleaving atoms into parts. Where there once was an electrically neutral atom, a positively charged ion and negatively charged electron (sometimes several) remain.

The result? The air itself becomes electrified.

Scientists call this region the ionosphere. The ionosphere doesn’t form a physically separated atmospheric layer – the charged particles float amongst their neutral neighbors, like bits of cookie dough in a pint of cookie dough ice cream. Nonetheless, they follow a very different set of rules.

Consider how the ionosphere moves. Charged particles are constrained by magnetism; like railroad cars, they trace Earth’s magnetic field lines back and forth unless something actively derails them. Neutral particles can cross those tracks unfazed – they’re more like passengers crisscrossing as they board and exit at the station.

The ionosphere also reflects radio signals, which pass right through the neutral atmosphere as if it was transparent. (In fact, radio is how the ionosphere was discovered .) Scientists still use ground-based radio waves to study the ionosphere from afar. Learning about the neutral atmosphere, however, usually requires going there – or looking down at it from above.

Despite their differences, the ionosphere and the neutral atmosphere are parts of a larger atmospheric system, where disturbances in one part have a way of spreading to the other. Their connection is explored in a new paper led by Scott England, space physicist at Virginia Tech in Blacksburg and co-investigator for NASA’s Global-scale Observations of the Limb and Disk, or GOLD mission, published in the Journal of Geophysical Research .

England and his coauthors combined ground-based radio signal measurements with special-purpose satellite observations to study whether Traveling Ionospheric Disturbances – waves regularly observed moving through the ionosphere – are at root the same event as Traveling Atmospheric Disturbances, pulses sometimes seen in the neutral atmosphere.

Traveling Ionospheric Disturbances, or TIDs, are giant undulations in the ionosphere, waves that stretch hundreds of miles from peak to peak. They’re are detected with ground-based radar beams, which bounce radars off the ionosphere to detect density enhancements move through.

Traveling Atmospheric Disturbances, or TADs, are gusts of wind that roll through the sky, pushing along neutral atoms as they go. TADs are harder to measure, best observed by flying within them – as some missions have – or by using indirect measures of airglow , the glimmer of oxygen and nitrogen in our atmosphere that brightens and dims as TADs move through it.

TIDs and TADs are measured in quite different ways, and it can be hard to compare across them. Still, many scientists have assumed that if one is present, the other is too.

“There is this assumption that they’re just the same thing,” said England. “But how robust is that assumption? It may be extremely good – but let’s check.”

England designed 3-day campaign to look for TIDs and TADs at the same time and same place.

TIDs were tracked from below, using ground-based radio receivers from stations across the Eastern U.S. Meanwhile, NASA’s Global-scale Observations of the Limb and Disk, or GOLD satellite, was looking for TADs from above, measuring airglow variations to track movements of the neutral atmosphere. But it took a little re-jiggering to see them. GOLD typically scans the whole western hemisphere once every half hour, but that’s too quick a glance at any one location to see a TAD.

“GOLD was never designed to see these things,” said England. “So we devised a campaign where we have it not do what it normally does.”

Instead, England directed one of GOLD’s telescopes to stare to along a strip of sky, increasing its detection power 100-fold. That strip is shown below in purple – GOLD’s search space for TADs. The region measured by ground-based radio receivers, which looked for TIDs, is shown in light blue.  The region where they overlapped was the focus of England’s study.

The radio receivers listened for changes in incoming signals, as these modulations could indicate a TID was passing by. The graph below shows the radar results from one of the three days in the campaign. The vertical axis represents latitude – higher up meaning more northern – and the horizontal axis represents time. The different colors show the strength of the signal modulation, dark red being the strongest.

Over a span of 12 hours, three stripes formed in the data. These were TIDs: pulses or density enhancements in the ionosphere moving southward over time.

Meanwhile, GOLD was watching light from oxygen and nitrogen to discern the motion of the neutral atmosphere. The graph below shows the results. Note that the latitudes GOLD measured range farther than the radar measurements, from 60 degrees to 10 degrees, but over a slightly shorter period of time, about 8 hours.

It was a weak signal, just above the ambient environmental noise. Still, the faint outlines of TADs – diagonal stripes in the GOLD data – appeared at the same time.

“It’s really at the limit of what GOLD could see – if it was any smaller than this, we wouldn’t see it,” England said.

Aligning the two datasets and correlating them, England found that both sets of ripples moved at about the same rate. Then, with the help of some mathematical models, they tested out the idea that atmospheric gravity waves could be the underlying cause of both.

Gravity waves – not to be confused with gravitational waves , caused by distant supernova explosions and black hole mergers – form when buoyancy pushes air up, and gravity pulls it back down. They’re often created when winds blow against mountain faces, pushing plumes of air upward. Those plumes soon fall back down, but like a line of dominos, the initial “push” cascades all the way to the upper atmosphere.

England and his coauthors linked up a mathematical model of the atmosphere with an airglow simulator. They then mimicked a gravity wave by introducing an artificial sine wave to the models. The resulting  simulated data produced similar “stripes,” both in the atmospheric model (TIDs) and the airglow simulator (TADs), indicating that gravity waves could indeed cause both.

So – are TIDs just TADs, as scientists assumed? While the pulses moved together, England’s team found that their amplitude, or size, were not as clearly related. Sometimes a large TID would be associated with a small TAD, and vice versa. Partly that’s because GOLD and the radio receivers don’t measure exact same altitudes – the radio receivers picked up a region about 40 miles above where GOLD could measure. But the largest contributor to that difference is probably the many other phenomena in the atmosphere that we don’t fully understand yet.

“And that makes what we’re looking at hard – but also interesting,” England added.

It will take more than three days of data to fully determine the relationship between TIDs and TADs. But England’s study provides something that virtually all scientists get excited about: a new tool for answering that question.

“We didn’t know if there would be a clear relationship between TIDs and TADs or not. And we certainly seem to have the ability to determine that now,” England said. “We just have to use the GOLD spacecraft instrument to do something we didn’t originally think of.”

13.1 Types of Waves

Section learning objectives.

By the end of this section, you will be able to do the following:

• Define mechanical waves and medium, and relate the two
• Distinguish a pulse wave from a periodic wave
• Distinguish a longitudinal wave from a transverse wave and give examples of such waves

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (A) examine and describe oscillatory motion and wave propagation in various types of media.

Section Key Terms

Mechanical waves.

What do we mean when we say something is a wave? A wave is a disturbance that travels or propagates from the place where it was created. Waves transfer energy from one place to another, but they do not necessarily transfer any mass. Light, sound, and waves in the ocean are common examples of waves. Sound and water waves are mechanical waves ; meaning, they require a medium to travel through. The medium may be a solid, a liquid, or a gas, and the speed of the wave depends on the material properties of the medium through which it is traveling. However, light is not a mechanical wave; it can travel through a vacuum such as the empty parts of outer space.

A familiar wave that you can easily imagine is the water wave. For water waves, the disturbance is in the surface of the water, an example of which is the disturbance created by a rock thrown into a pond or by a swimmer splashing the water surface repeatedly. For sound waves, the disturbance is caused by a change in air pressure, an example of which is when the oscillating cone inside a speaker creates a disturbance. For earthquakes, there are several types of disturbances, which include the disturbance of Earth’s surface itself and the pressure disturbances under the surface. Even radio waves are most easily understood using an analogy with water waves. Because water waves are common and visible, visualizing water waves may help you in studying other types of waves, especially those that are not visible.

Water waves have characteristics common to all waves, such as amplitude , period , frequency , and energy , which we will discuss in the next section.

Misconception Alert

Many people think that water waves push water from one direction to another. In reality, however, the particles of water tend to stay in one location only, except for moving up and down due to the energy in the wave. The energy moves forward through the water, but the water particles stay in one place. If you feel yourself being pushed in an ocean, what you feel is the energy of the wave, not the rush of water. If you put a cork in water that has waves, you will see that the water mostly moves it up and down.

[BL] [OL] [AL] Ask students to give examples of mechanical and nonmechanical waves.

Pulse Waves and Periodic Waves

If you drop a pebble into the water, only a few waves may be generated before the disturbance dies down, whereas in a wave pool, the waves are continuous. A pulse wave is a sudden disturbance in which only one wave or a few waves are generated, such as in the example of the pebble. Thunder and explosions also create pulse waves. A periodic wave repeats the same oscillation for several cycles, such as in the case of the wave pool, and is associated with simple harmonic motion. Each particle in the medium experiences simple harmonic motion in periodic waves by moving back and forth periodically through the same positions.

[BL] Any kind of wave, whether mechanical or nonmechanical, or transverse or longitudinal, can be in the form of a pulse wave or a periodic wave.

Consider the simplified water wave in Figure 13.2 . This wave is an up-and-down disturbance of the water surface, characterized by a sine wave pattern. The uppermost position is called the crest and the lowest is the trough . It causes a seagull to move up and down in simple harmonic motion as the wave crests and troughs pass under the bird.

Longitudinal Waves and Transverse Waves

Mechanical waves are categorized by their type of motion and fall into any of two categories: transverse or longitudinal. Note that both transverse and longitudinal waves can be periodic. A transverse wave propagates so that the disturbance is perpendicular to the direction of propagation. An example of a transverse wave is shown in Figure 13.3 , where a woman moves a toy spring up and down, generating waves that propagate away from herself in the horizontal direction while disturbing the toy spring in the vertical direction.

In contrast, in a longitudinal wave , the disturbance is parallel to the direction of propagation. Figure 13.4 shows an example of a longitudinal wave, where the woman now creates a disturbance in the horizontal direction—which is the same direction as the wave propagation—by stretching and then compressing the toy spring.

Tips For Success

Longitudinal waves are sometimes called compression waves or compressional waves , and transverse waves are sometimes called shear waves .

Teacher Demonstration

Transverse and longitudinal waves may be demonstrated in the class using a spring or a toy spring, as shown in the figures.

Waves may be transverse, longitudinal, or a combination of the two . The waves on the strings of musical instruments are transverse (as shown in Figure 13.5 ), and so are electromagnetic waves, such as visible light. Sound waves in air and water are longitudinal. Their disturbances are periodic variations in pressure that are transmitted in fluids.

Sound in solids can be both longitudinal and transverse. Essentially, water waves are also a combination of transverse and longitudinal components, although the simplified water wave illustrated in Figure 13.2 does not show the longitudinal motion of the bird.

Earthquake waves under Earth’s surface have both longitudinal and transverse components as well. The longitudinal waves in an earthquake are called pressure or P-waves, and the transverse waves are called shear or S-waves. These components have important individual characteristics; for example, they propagate at different speeds. Earthquakes also have surface waves that are similar to surface waves on water.

Energy propagates differently in transverse and longitudinal waves. It is important to know the type of the wave in which energy is propagating to understand how it may affect the materials around it.

Watch Physics

Introduction to waves.

This video explains wave propagation in terms of momentum using an example of a wave moving along a rope. It also covers the differences between transverse and longitudinal waves, and between pulse and periodic waves.

• After a compression wave, some molecules move forward temporarily.
• After a compression wave, some molecules move backward temporarily.
• After a compression wave, some molecules move upward temporarily.
• After a compression wave, some molecules move downward temporarily.

Fun In Physics

The physics of surfing.

Many people enjoy surfing in the ocean. For some surfers, the bigger the wave, the better. In one area off the coast of central California, waves can reach heights of up to 50 feet in certain times of the year ( Figure 13.6 ).

How do waves reach such extreme heights? Other than unusual causes, such as when earthquakes produce tsunami waves, most huge waves are caused simply by interactions between the wind and the surface of the water. The wind pushes up against the surface of the water and transfers energy to the water in the process. The stronger the wind, the more energy transferred. As waves start to form, a larger surface area becomes in contact with the wind, and even more energy is transferred from the wind to the water, thus creating higher waves. Intense storms create the fastest winds, kicking up massive waves that travel out from the origin of the storm. Longer-lasting storms and those storms that affect a larger area of the ocean create the biggest waves since they transfer more energy. The cycle of the tides from the Moon’s gravitational pull also plays a small role in creating waves.

Actual ocean waves are more complicated than the idealized model of the simple transverse wave with a perfect sinusoidal shape. Ocean waves are examples of orbital progressive waves , where water particles at the surface follow a circular path from the crest to the trough of the passing wave, then cycle back again to their original position. This cycle repeats with each passing wave.

As waves reach shore, the water depth decreases and the energy of the wave is compressed into a smaller volume. This creates higher waves—an effect known as shoaling .

Since the water particles along the surface move from the crest to the trough, surfers hitch a ride on the cascading water, gliding along the surface. If ocean waves work exactly like the idealized transverse waves, surfing would be much less exciting as it would simply involve standing on a board that bobs up and down in place, just like the seagull in the previous figure.

Additional information and illustrations about the scientific principles behind surfing can be found in the “Using Science to Surf Better!” video.

• The surfer would move side-to-side/back-and-forth vertically with no horizontal motion.
• The surfer would forward and backward horizontally with no vertical motion.

Check Your Understanding

Use these questions to assess students’ achievement of the section’s Learning Objectives. If students are struggling with a specific objective, these questions will help identify such objective and direct them to the relevant content.

• A wave is a force that propagates from the place where it was created.
• A wave is a disturbance that propagates from the place where it was created.
• A wave is matter that provides volume to an object.
• A wave is matter that provides mass to an object.
• No, electromagnetic waves do not require any medium to propagate.
• No, mechanical waves do not require any medium to propagate.
• Yes, both mechanical and electromagnetic waves require a medium to propagate.
• Yes, all transverse waves require a medium to travel.
• A pulse wave is a sudden disturbance with only one wave generated.
• A pulse wave is a sudden disturbance with only one or a few waves generated.
• A pulse wave is a gradual disturbance with only one or a few waves generated.
• A pulse wave is a gradual disturbance with only one wave generated.

What are the categories of mechanical waves based on the type of motion?

• Both transverse and longitudinal waves
• Only longitudinal waves
• Only transverse waves
• Only surface waves

In which direction do the particles of the medium oscillate in a transverse wave?

• Perpendicular to the direction of propagation of the transverse wave
• Parallel to the direction of propagation of the transverse wave

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• Authors: Paul Peter Urone, Roger Hinrichs
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• Book title: Physics
• Publication date: Mar 26, 2020
• Location: Houston, Texas
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The Nature of Waves

A wave is a disturbance that propagates through a medium. There are three words in that definition that may need unpacking: disturbance, propagate, and medium.

• a change in a kinematic variable like position, velocity, or acceleration;
• a change in an intensive property like pressure, density, or temperature;
• a change in field strength like electric field strength, magnetic field strength, or gravitational field strength.
• To propagate , in the sense used in this definition, is to transmit the influence of something in a particular direction. Synonyms for propagate include spread, transmit, communicate, and broadcast. The noun form of the word is propagation .
• A medium is the substance through which a wave can propagate. Water is the medium of ocean waves. Air is the medium through which we hear sound waves. The electric and magnetic fields are the medium of light. People are the medium of a stadium wave. The Earth is the medium of seismic waves (earthquake waves). Cell membranes are the medium of nerve impulses. Transmission lines are the medium of alternating current electric power. Medium is the singuar form of the noun. Media is the plural form (although mediums is prefered by some people).

Let's list a few key examples of wave phenomena and then connect them to this definition. The first example that comes to mind when most people hear the word wave are the kinds of waves that one sees on the surface of a body of water: deep water waves in the ocean or ripples in a puddle. The most important kinds of waves for humans are the waves we use to sense the world around us: sound and light.

Imagine a calm pool. The surface is flat and smooth. Drop a rock into it. Kerploop. The surface is now disturbed. It is higher than normal in some places and lower than normal in others. The disturbed water at the point of impact disturbs the water next to it, which in turn disturbs the water next to it, which disturbs the water next to it, and so on. The disturbance spreads outward, transmits, or propagates. The medium through which this disturbance propagates is the surface of the water.

Imagine a quiet room. The air inside is still. Drop a book onto a table in that room. Thwap. The air between the book and the table is squeezed out in a fraction of a second. The air pressure in that rapidly decreasing gap rises above normal and then rebounds. The rise and fall of pressure is like the rise and fall of the surface of the pool in the previous example. The air under the book bumps the air on the edges of the book, which bumps the air next to it, which bumps the air next to it, and so on. The medium through which this disturbance propagates is the air.

Those were the easy examples. Water waves and sound waves are examples of mechanical waves — waves that propagate through a material medium. Light is not so easy to understand as a wave, which is why there are multiple sections of this book devoted to it. Still, I am going to try to describe it briefly.

Imagine a dark cavern, deep within the Earth. The electric and magnetic fields inside are relatively static and unchanging. Strike a match. Skeerach. The atoms of carbon in the wood of the matchstick combine with the atoms of oxygen in the air releasing heat. The heat agitates the atoms of the combustion products resulting in the phenomenon known as fire. The electrons bound to the rapidly vibrating atoms disturb the electric and magnetic fields in the space surrounding them. These fields are "elastic" in a sense. A wiggle in the fields in one place causes a wiggle in the fields nearby, which causes a wiggle in the fields nearby, and so on. These wiggles eventually make it to your eye, which you perceive as light. The electric and magnetic fields that fill all of space are the medium.

essential property

Waves transfer energy, momentum, and information, but not mass.

A naive description of a wave is that it has something to do with motion. But the motion of a wave on the water is not the same as the motion of the water from a hose. When waves move over the surface of the ocean, where does the ocean go? Nowhere. When waves reach the shore, does the water accumulate into great heaps? No. The water moves in and out, and the ocean stays behind. Even when huge tsunamis strike, the wall of water deposited on the land eventually drains back into the sea. In this case, no net transfer of mass has occurred.

Compare this to the water from a hose. The water comes pouring out the open end and stays where it lands forming a puddle or drains away to some other location. It most certainly does not jump back into the hose. In this case, mass has been transferred from one location to another.

Any sensible person who owns waterfront property should be familiar with the word erosion. Ocean waves (or waves on the Great Lakes for that matter) break on the shore, beating the rock and soil into submission and pulling it away. This material will never return. (If there were no plate tectonic forces lifting the land up in some places or volcanoes creating new land in others, the Earth would be covered in a global sea of uniform depth.) A force ( F ) has been exerted and mass has been displaced ( ∆ s ). Work has been done ( W  =  F ∆ s ). The ability to do work is one definition of energy ( W  = ∆ E ). Thus waves transfer energy.

Sticking with the example of ocean waves, anyone who surfs knows that waves transfer momentum. I have less to say on this subject.

Sound and light are the two primary examples of the way we gather information around us as humans. We have specialized sensory organs called ears and eyes for doing just that.

Here's a list of some phenomena or activities that satisfy the definition of a wave given above.

• including hock waves
• Radio waves
• Visible light
• Ultraviolet
• Tsunamis (tidal waves)
• Ripples (capillary waves)
• P waves (primary waves, pressure waves)
• S waves (secondary waves, shear waves)
• R waves (Rayleigh waves, ground roll)
• L waves (Love waves)
• A fluttering flag
• Snapping a sheet when making a bed
• Nerve impulses
• Peristalsis
• Heart contractions
• Snakes, eels, etc
• Worms, slugs, etc.
• Centipedes, millipedes, caterpillars, etc.
• Plucking, bowing, or striking a guitar, violin, or piano string
• Casting loops when fly fishing
• Cracking a whip
• Gravitational waves (as described in general relativity, not to be confused with gravity waves in water)
• Matter waves (quantum mechanical waves, de Broglie waves)
• Dominoes (as a show, not as a game)
• Stadium wave (Mexican wave, the wave)
• Newton's cradle (paid link)

not examples

Just because the word wave is used doesn't mean the thing being described is a wave in the sense used in this book.

• Waving as a signal to get someone's attention or to greet them or to say goodbye is not a wave. It does not propagate in a direction. Just because you wave at me does not mean that I have to start waving followed by a person behind me and the person behind them and the person behind them.
• A permanent wave set in a person's hair is not a wave. The term is almost an oxymoron. Nothing's moving if a thing is permanent. Also, you getting a wave set in your hair does not result in the people nearest you getting one followed by the people next to them getting one, and so on, until the whole globe is filled with wavy haired people.
• Wheat, or any other tall grass, is sometimes said to wave when gusts of wind pass over it. That bulk flow of matter is not a wave and neither is the response of the wheat.
• A heat wave is a meteorological term referring to a prolonged period of unusually high temperature. This definition has no connection to a phenomenon that propagates. Just because it's hot for a long period in one location does not imply that the heat wave will propagate to another location. It's actually sort of the opposite. A heat wave is often a region where the hot air is "stuck". The opposite of a heat wave could be called a cold wave, but it's usually described a cold snap (at least in the dialect of English I'm used to hearing). This should indicate that neither one of these phenomena is really a wave. Sometimes infrared radiation is described colloquially as heat waves, but that's not the right term. The same goes for rising thermals in the desert. That shimmering effect sometimes seen on the horizon is turbulent air of different density streaming upward and not a wave. Waves do not transfer mass.
• A crime wave is like a heat wave, but for crime. Since heat waves aren't waves, neither are crime waves.
• Making waves, meaning to stir up trouble, is not an example of a wave — and don't you disagree with me you trouble maker.

Classification of waves

Waves can be classified according to the medium through which they propagate.

by the type of disturbance

Waves can be classified according to the type of disturbance — meaning its relative direction or shap. There is a lot that can be said about this organizational scheme. I'm starting this part of this section with a quick summary in table form followed by a rather detailed follow up.

transverse waves

A transverse wave is one in which the direction of the disturbance is perpendicular to the direction of propagation. The word transverse describes something pointing in a sideways or lateral direction. As dynamic phenomena, waves are better represented with animations than with static images. Click on the static image below to see a transverse wave in action.

A cartoon representation of this kind of wave is your classic wiggly line. People with a bit of math knowledge will tell you they drew a sine curve. Those with a little bit more math knowledge will say they drew a sine or cosine curve.

The high parts on a curve like this are called crests . The low parts are called troughs . Since directions like up and down don't always make sense for waves, what the parts really represent are the maximal changes. The points labeled crests are points corresponding to a maximal increase of the changing quantity in a whatever direction is decided to be positive. The points labeled troughs are the points corresponding to the maximal change in the opposite direction.

Pronouncing words ending in -ough in English is often a mystery. The word trough rhymes with off. A trough is what one uses to provide food and water to livestock and other domesticated animals — typically a long, narrow open container that an animal would dip its head down into. The word crest rhymes with best. A crest is something at the top of something. Many birds, usually male birds, have crests. Hills and mountains are are sometimes said to have crests. The crest on a men's sports jacket or a school uniform gets its name from the heraldic crests that were originally worn on knight's helmets above the visor. Crests are up high. Troughs are down low.

The most important example of a transverse wave for humans is light. Most of what I am about to say in the following bullets will really be discussed elsewhere in this book.

• Showing that light is a just wave was not easy before the 20th century. Now that we have easy access to lasers in the 21st century, it's less of a problem. Light can be made to interfere with itself and produce a pattern of what are called interference fringes . A laser and two or more closely spaced openings are all that is needed. The iridescence seen when gasoline is spilled on water, in some insects like scarab beetles and butterflies, and in pearls and the shells of mollusks is caused by thin film interference . Observing this wave behavior of light requires no special technology.
• Showing that light is a transverse wave was was also not easy before the 20th century. Now that we have easy access to polarized sunglasses and polarized electronic displays in the 21st century, it's less of a problem. Light can be shown to exhibit polarization . Try looking at certain electronic displays with polarized sunglasses. If the orientation of the sunglasses is perpendicular to the orientation of the display, the display will look dark (or really screwed up). If the orientation is parallel, the display will look normal (or closer to normal than when they were perpendicular).

Lots of musical instruments make use of transverse waves to generate their characteristic sound.

• The source of the sound that comes out of violins, guitars, pianos and other chordophones is the side to side motion of a nylon or metal string (or in the olden days, dried animal intestines). The parts of the string vibrate side to side, but the wave travels along the length of the string. These two directions are perpendicular, which makes the waves transverse. The vibrations of the string are also transmitted into the wooded bodies or sound boards of these instruments. These flat wooden parts are driven to flex in and out, but the energy propagates across the surface. The two directions here are also perpendicular.
• The source of the sound that comes out of drum heads, kazoos or other membranophones is the in and out vibration of some flat, membrane-like structure. The waves produced by striking, stroking, or humming into these devices generates waves that crisscross the object. Once again, the disturbance is perpendicular to the propagation.
• Most percussion instruments that are not drums are classified as idiophones . Cymbals, triangles, and xylophones produce sound by the vibration of the entire object or a piece that is not a string, membrane, or column of air. The waves set up in many of these instruments are transverse, but because the class is so large and varied there is probably an exception out there somewhere.

Some animals propel themselves by sending transverse waves down the length of their bodies.

• Fish use a variety of means for getting around but long, thin, tubular fish like eels, lamprey, and dogfish are what comes to mind when I think about locomotion by transverse waves. A wave of side to side motion starts at the head and propagates backward along the spine. This propels the fish forward.
• Snakes also have several mechanisms for propelling themselves. The one that is considered most "normal" is called lateral undulation and has the classic look of a transverse wave in a one-dimensional medium. Much like the fish described above, a wave starts at the head as side to side motion and propagates backward down the length of the snake. A fancier kind of locomotion that relies on transverse waves is called sidewinding and the snakes that use it live in sandy deserts or slippery mud flats — anywhere getting a good grip on the ground is difficult. It's still an example of a transverse wave, but it propels the snake diagonally instead of forward relative to its body axis.

longitudinal waves

• pressure, compression, density
• aerophones - vibrating columns of air (horns, whistles, organ pipes )
• primary (P) pressure
• invertebrates (worms)
• traffic jams
• density waves in spiral galaxies generate the arms
• compressions (a.k.a. condensation): the pressed part, the greatest positive pressure change, a region where the medium is under compression
• rarefactions (a.k.a. dilations): the stretched part, the lowest negative pressure change, a region where the medium is under tension

complex waves

classed by orientation of change

• P rimary (surface, compression, P ressure)
• S econdary (transverse, S hear), can't propagate through liquids
• L ove, ( L ateral shear)
• R ayleigh, (elliptical, plate waves, ground R oll), something like ocean waves, but elliptical instead of circular

torsional waves

By duration.

classified by duration

by appearance

Waves can be classified according to what they appear to be doing.

Now look at these pretty, moving pictures.

Travelling Wave

When something about the physical world changes, the information about that disturbance gradually moves outwards, away from the source, in every direction. As the information travels, it travels in the form of a wave. Sound to our ears, light to our eyes, and electromagnetic radiation to our mobile phones are all transported in the form of waves. A good visual example of the propagation of waves is the waves created on the surface of the water when a stone is dropped into a lake. In this article, we will be learning more about travelling waves.

Describing a Wave

A wave can be described as a disturbance in a medium that travels transferring momentum and energy without any net motion of the medium. A wave in which the positions of maximum and minimum amplitude travel through the medium is known as a travelling wave. To better understand a wave, let us think of the disturbance caused when we jump on a trampoline. When we jump on a trampoline, the downward push that we create at a point on the trampoline slightly moves the material next to it downward too.

When the created disturbance travels outward, the point at which our feet first hit the trampoline recovers moving outward because of the tension force in the trampoline and that moves the surrounding nearby materials outward too. This up and down motion gradually ripples out as it covers more area of the trampoline. And, this disturbance takes the shape of a wave.

Following are a few important points to remember about the wave:

• The high points in the wave are known as crests and the low points in the wave are known as troughs.
• The maximum distance of the disturbance of the wave from the mid-point to either the top of the crest or to the bottom of a trough is known as amplitude.
• The distance between two adjacent crests or two adjacent troughs is known as a wavelength and is denoted by 𝛌.
• The time interval of one complete vibration is known as a time period.
• The number of vibrations the wave undergoes in one second is known as a frequency.
• The relationship between the time period and frequency is given as follows:
• The speed of a wave is given by the equation

Different Types of Waves

Different types of waves exhibit distinct characteristics. These characteristics help us distinguish between wave types. The orientation of particle motion relative to the direction of wave propagation is one way the traveling waves are distinguished. Following are the different types of waves categorized based on the particle motion:

• Pulse Waves – A pulse wave is a wave comprising only one disturbance or only one crest that travels through the transmission medium.
• Continuous Waves – A continuous-wave is a waveform of constant amplitude and frequency.
• Transverse Waves – In a transverse wave, the motion of the particle is perpendicular to the direction of propagation of the wave.
• Longitudinal Waves – Longitudinal waves are the waves in which the motion of the particle is in the same direction as the propagation of the wave.

Although they are different, there is one property common between them and that is the transportation of energy. An object in simple harmonic motion has an energy of

Constructive and Destructive Interference

A phenomenon in which two waves superimpose to form a resultant wave of lower, greater, or the same amplitude is known as interference. Constructive and destructive interference occurs due to the interaction of waves that are correlated with each other either because of the same frequency or because they come from the same source. The interference effects can be observed in all types of waves such as gravity waves and light waves.

According to the principle of superposition of the waves , when two or more propagating waves of the same type are incidents on the same point, the resultant amplitude is equal to the vector sum of the amplitudes of the individual waves. When a crest of a wave meets a crest of another wave of the same frequency at the same point, then the resultant amplitude is the sum of the individual amplitudes. This type of interference is known as constructive interference. If a crest of a wave meets a trough of another wave, then the resulting amplitude is equal to the difference in the individual amplitudes and this is known as destructive interference.

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Watch the video and understand longitudinal and transverse waves in detail.

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Acoustics and Vibration Animations

Daniel A. Russell , Graduate Program in Acoustics, The Pennsylvania State University

The content of this page was originally posted on April 16, 2002 . Animations and text were updated on February 18, 2015 . The HTML code was modified to be HTML5 compliant on March 18, 2013.

What is a Wave?

Definition of a wave.

Webster's dictionary defines a wave as:

The most important part of this definition is that a wave is a disturbance or variation which travels through a medium. The medium through which the wave travels may experience some local oscillations as the wave passes, but the particles in the medium do not travel with the wave. The disturbance may take any of a number of shapes, from a finite width pulse to an infinitely long sine wave.

Examples which illustrate the definition

Have you ever "done the wave" as part of a large crowd at a football or baseball game? A group of people jumps up and sits back down, some nearby people see them and they jump up, some people further away follow suit and pretty soon you have a wave travelling around the stadium. The wave is the disturbance (people jumping up and sitting back down), and it travels around the stadium. However, none of the individual people in the stadium are carried around with the wave as it travels - they all remain at their seats. Check out this real-life example by a military precision drill team (form Physics Footnotes )

Sound waves in air behave in much the same way. As the wave pulse passes through, the particles in the air oscillate back and forth about their equilibrium positions but it is the disturbance which travels, not the individual particles in the medium. There are several other examples of wave types which can propagate through a mechanical medium.

Transverse waves on a string are another example. The string is displaced up and down as the wave pulse travels from left to right, but the string itself does not experience any net motion. I have other animations that illustrate what happens when transverse waves on strings reflect from hard and soft boundaries , or from more general impedance boundaries .

Here is a more detailed example of a longitudinal wave traveling through a material medium. While the wave exampels above were pulses (with a finite duration), this wave is a continuous sinusoidal wave, with regions of compression (where the particles are squished closer together) alternating with regions of rarefaction (where particles are spread farther apart). Red dots (and arrows) show that individual particles simply oscillate back and forth about their equilibrium positions while the wave disturbance propagates through the medium.

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14.1: Characteristics of a wave

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Definition and types of waves

A traveling wave is a disturbance that travels through a medium. Consider the waves made by fans at a soccer game, as in Figure \(\PageIndex{1}\). The fans can be thought of as the medium through which the wave propagates. The elements of the medium may oscillate about an equilibrium position (the fans move a short distance up and down), but they do not travel with the wave (the fans do not move horizontally with the wave).

Consider the ripples (waves) made by a rock dropped in a pond (Figure \(\PageIndex{2}\)). The ripples travel outwards from where the rock was dropped, but the water itself does not move outwards. The individual water molecules will move in small circles about an equilibrium position, but they do not move along with the waves.

We can distinguish between two classes of waves, based on the motion of the medium through which it propagates. With transverse waves , the elements of the medium oscillate back and forth in a direction perpendicular to the motion of the wave. For example, if you attach a horizontal rope to a wall and move the other end up and down (Figure \(\PageIndex{3}\)), you can create a disturbance (a wave) that travels horizontally along the rope. The parts of the rope do not move horizontally; they only move up and down, about some equilibrium position.

With longitudinal waves , the elements of the medium oscillate back and forth in the same direction as the motion of the wave. If you clap your hands, you will create a pressure disturbance in the air that will propagate; this is what we call sound (a sound wave). The air molecules oscillate about an equilibrium position in the same direction as the wave propagates, but they do not move with the wave.

Furthermore, we can distinguish between “travelling waves”, in which a disturbance propagates through a medium, and “standing waves”, which do not transport energy through the medium (for example, a vibrating string on a violin).

Exercise \(\PageIndex{1}\)

Are the waves propagating through a slinky when you compress and elongate it (Figure \(\PageIndex{5}\)) transverse or longitudinal?

• Longitudinal

Physically, a wave can only propagate through a medium if the medium can be deformed. When a particle in the medium is disturbed from its equilibrium position, it will experience a restoring force that acts to bring it back to its equilibrium position. Often, if the displacement of the particle from the equilibrium is small, the magnitude of that force is proportional to the displacement. Thus, as we will see, we can model the propagation of waves by treating the particles in the medium as simple harmonic oscillators.

A source of energy is required in order to deform the medium and generate a wave. For example, that source of energy could be a speaker creating sound waves by pushing a membrane back and forth; speakers require energy, and are often rated by the electrical power that they convert into sound waves (e.g. a \(50\text{W}\) speaker consumes \(50\text{W}\) of electrical power to produce sound).

Description of a wave

In this chapter, we will mostly discuss how to describe sinusoidal waves; those for which the displacement of particles in the medium can be described by a sinusoidally-varying function of position. As we will see, more complicated waves can always be described as if they are the combination of multiple sine waves. We can use several quantities to describe a traveling wave, which are illustrated in Figure \(\PageIndex{7}\):

• The wavelength , \(\lambda\) , is the distance between two successive maxima (“peaks”) or minima (“troughs”) in the wave.
• The amplitude , \(A\) , is the maximal distance that a particle in the medium is displaced from its equilibrium position.
• The velocity , \(\vec v\) , is the velocity with which the disturbance propagates through the medium.
• The period , \(T\) , is the time it takes for two successive maxima (or minima) to pass through the same point in the medium.
• The frequency , \(f\) , is the inverse of the period ( \(f=1/T\) ).

The wavelength, speed, and period of the wave are related, since the amount of time that it takes for two successive maxima of the wave to pass through a given point will depend on the speed of the wave and the distance between maxima, \(\lambda\) . Since it takes a time, \(T\) , for two maxima a distance \(\lambda\) apart to pass through a given point in the medium, the speed of the wave is given by:

\[v=\frac{\lambda}{T}=\lambda f\]

Thus, of the three quantities (speed, period/frequency, and wavelength), only two are independent, as the third quantity must depend on the value of the other two. The speed of a wave depends on the properties of the medium through which the wave propagates and not on the mechanism that is generating the wave . For example, the speed of sound waves depends on the pressure, density, and temperature of the air through which they propagate, and not on what is making the sound. When a mechanism generates a wave, that mechanism usually determines the frequency of the wave (e.g. frequency with which the hand in Figure \(\PageIndex{7}\) moves up and down), the speed is determined by the medium, and the wavelength can be determined from Equation 14.1.1 .

Exercise \(\PageIndex{2}\)

What can you say about the sound emitted by a cello versus that emitted by a violin?

• The sound from the violin has a higher frequency.
• The sound from the cello has a longer wavelength.
• The sound from both instruments propagates at the same speed.
• All of the above.

Travelling Wave

Definition: Travelling wave is a temporary wave that creates a disturbance and moves along the transmission line at a constant speed. Such type of wave occurs for a short duration (for a few microseconds) but cause a much disturbance in the line. The transient wave is set up in the transmission line mainly due to switching, faults and lightning.

The travelling wave plays a major role in knowing the voltages and currents at all the points in the power system. These waves also help in designing the insulators, protective equipment, the insulation of the terminal equipment, and overall insulation coordination.

Specifications of Travelling Wave

The travelling wave can be represented mathematically in a number of ways. It is most commonly represents in the form of infinite rectangular or step wave. A travelling wave is characterised by four specifications as illustrated in the figure below.

Crest – it is the maximum aptitude of the wave, and it is expressed in kV or kA.

Front – It is the portion of the wave before the crest and is expressed in time from the beginning of the wave to the crest value in milliseconds or µs.

Tail – The tail of the wave is the portion beyond the crest. It is expressed in time from the beginning of the wave to the point where the wave has reduced to 50% of its value at its crest.

Polarity – Polarity of the crest voltage and value. A positive wave of 500 kV crest 1 µs front and 25 µs tail will be presented as +500/1.0/25.0.

Surge is a type of travelling wave which is caused because of the movement of charges along the conductor. The surge generates because of a sudden vary steep rise in voltage (the steep front) followed by a gradual decay in voltage (the surge tail). These surges reach the terminal apparatus such as cable boxes, transformers or switchgear, and may damage them if they are not properly protected.

Travelling Wave on Transmission Line

The transmission line is a distributed parameter circuit and its support the wave of voltage and current. A circuit with distributed parameter has a finite velocity of electromagnetic field propagation. The switching and lightning operation on such types of circuit do not occur simultaneously at all points of the circuit but spread out in the form of travelling waves and surges.

When a transmission line is suddenly connected to a voltage source by the closing of a switch the whole of the line in not energised at once, i.e., the voltage does not appear instantaneously at the other end. This is due to the presence of distributed constants (inductance and capacitance in a loss-free line).

Considered a long transmission line having a distributed parameter inductance (L) and capacitance (C). The long transmission line is divided into small section shown in the figure below.The S is the switch used for closing or opening the surges for switching operation. When the switch is closed the L1 inductance act as an open circuit and C 1 act as a short circuit. At the same instant, the voltage at the next section cannot be charged because the voltage across the capacitor C 1 is zero.

So unless the capacitor C 1 is charged to some value the charging of the capacitor C 2 through L 2 is not possible which will obviously take some time. The same argument applies to the third section, fourth section, and so on. The voltage at the section builds up gradually. This gradual build up of voltage over the transmission conductor can be regarded as though a voltage wave is travelling from one end to the other end and the gradual charging of the voltage is due to associate current wave.

The current wave, which is accompanied by voltage wave steps up a magnetic field in the surrounding space. At junctions and terminations, these waves undergo reflection and refraction. The network has a large line and junction the number of travelling waves initiated by a single incident wave and will increase at a considerable rate as the wave split and multiple reflections occurs. The total energy of the resultant wave cannot exceed the energy of the incident wave.

Related terms:

• Half Wave and Full Wave Rectifier
• Difference Between Electromagnetic Wave and Matter Wave
• Lap & Wave Winding
• Difference Between Lap & Wave Winding
• Full Wave Bridge Rectifier

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Module 4 Waves

Wave motion transfers energy from one point to another, usually without permanent displacement of the particles of the medium.

Learning Objectives

Describe process of energy and mass transfer during wave motion

Key Takeaways

• A wave can be thought of as a disturbance or oscillation that travels through space-time, accompanied by a transfer of energy.
• The direction a wave propagates is perpendicular to the direction it oscillates for transverse waves.
• A wave does not move mass in the direction of propagation; it transfers energy.
• medium : The material or empty space through which signals, waves or forces pass.
• direction of propagation : The axis along which the wave travels.
• wave : A moving disturbance in the energy level of a field.

Vibrations and waves are extremely important phenomena in physics. In nature, oscillations are found everywhere. From the jiggling of atoms to the large oscillations of sea waves, we find examples of vibrations in almost every physical system. In physics a wave can be thought of as a disturbance or oscillation that travels through space-time, accompanied by a transfer of energy. Wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium —that is, with little or no associated mass transport. They consist, instead, of oscillations or vibrations around almost fixed locations.

The emphasis of the last point highlights an important misconception of waves. Waves transfer energy not mass. An easy way to see this is to imagine a floating ball a few yards out to sea. As the waves propagate (i.e., travel) towards the shore, the ball will not come towards the shore. It may come to shore eventually due to the tides, current or wind, but the waves themselves will not carry the ball with them. A wave only moves mass perpendicular to the direction of propagation—in this case up and down, as illustrated in the figure below:

Wave motion : The point along the axis is analogous to the floating ball at sea. We notice that while it moves up and down it does not move in the direction of the wave’s propagation.

A wave can be transverse or longitudinal depending on the direction of its oscillation. Transverse waves occur when a disturbance causes oscillations perpendicular (at right angles) to the propagation (the direction of energy transfer). Longitudinal waves occur when the oscillations are parallel to the direction of propagation. While mechanical waves can be both transverse and longitudinal, all electromagnetic waves are transverse. Sound, for example, is a longitudinal wave.

The description of waves is closely related to their physical origin for each specific instance of a wave process. For example, acoustics is distinguished from optics in that sound waves are related to a mechanical rather than an electromagnetic (light) wave transfer caused by vibration. Therefore, concepts such as mass, momentum, inertia or elasticity become crucial in describing acoustic (as distinct from optic) wave processes. This difference in origin introduces certain wave characteristics particular to the properties of the medium involved. In this chapter we will closely examine the difference between longitudinal and transverse waves along with some of the properties they possess. We will also learn how waves are fundamental in describing motion of many applicable physical systems.

The Wave Equation : A brief introduction to the wave equation, discussing wave velocity, frequency, wavelength, and period.

Transverse Waves

Transverse waves propagate through media with a speed [latex]\vec{\text{v}}_\text{w}[/latex] orthogonally to the direction of energy transfer.

Describe properties of the transverse wave

• Transverse waves oscillate in the z-y plane but travel along the x axis.
• A transverse wave has a speed of propagation given by the equation v = fλ.
• The direction of energy transfer is perpendicular to the motion of the wave.
• wavelength : The length of a single cycle of a wave, as measured by the distance between one peak or trough of a wave and the next; it is often designated in physics as λ, and corresponds to the velocity of the wave divided by its frequency.
• trough : A long, narrow depression between waves or ridges.
• speed of propagation : The speed at which a wave moves through a medium.
• crest : The ridge or top of a wave.
• transverse wave : Any wave in which the direction of disturbance is perpendicular to the direction of travel.

A transverse wave is a moving wave that consists of oscillations occurring perpendicular (or right angled) to the direction of energy transfer. If a transverse wave is moving in the positive x -direction, its oscillations are in up and down directions that lie in the y–z plane. Light is an example of a transverse wave. For transverse waves in matter, the displacement of the medium is perpendicular to the direction of propagation of the wave. A ripple on a pond and a wave on a string are easily visualized transverse waves.

Transverse waves are waves that are oscillating perpendicularly to the direction of propagation. If you anchor one end of a ribbon or string and hold the other end in your hand, you can create transverse waves by moving your hand up and down. Notice though, that you can also launch waves by moving your hand side-to-side. This is an important point. There are two independent directions in which wave motion can occur. In this case, these are the y and z directions mentioned above. depicts the motion of a transverse wave. Here we observe that the wave is moving in t and oscillating in the x-y plane. A wave can be thought as comprising many particles (as seen in the figure) which oscillate up and down. In the figure we observe this motion to be in x-y plane (denoted by the red line in the figure). As time passes the oscillations are separated by units of time. The result of this separation is the sine curve we expect when we plot position versus time.

Sine Wave : The direction of propagation of this wave is along the t axis.

When a wave travels through a medium–i.e., air, water, etc., or the standard reference medium (vacuum)–it does so at a given speed: this is called the speed of propagation. The speed at which the wave propagates is denoted and can be found using the following formula:

[latex]\text{v}=\text{f} \lambda[/latex]

where v is the speed of the wave, f is the frequency , and is the wavelength. The wavelength spans crest to crest while the amplitude is 1/2 the total distance from crest to trough. Transverse waves have their applications in many areas of physics. Examples of transverse waves include seismic S (secondary) waves, and the motion of the electric (E) and magnetic (M) fields in an electromagnetic plane waves, which both oscillate perpendicularly to each other as well as to the direction of energy transfer. Therefore an electromagnetic wave consists of two transverse waves, visible light being an example of an electromagnetic wave.

Wavelength and Amplitude : The wavelength is the distance between adjacent crests. The amplitude is the 1/2 the distance from crest to trough.

Two Types of Waves: Longitudinal vs. Transverse : Even ocean waves!

Longitudinal Waves

Longitudinal waves, sometimes called compression waves, oscillate in the direction of propagation.

Give properties and provide examples of the longitudinal wave

• While longitudinal waves oscillate in the direction of propagation, they do not displace mass since the oscillations are small and involve an equilibrium position.
• The longitudinal ‘waves’ can be conceptualized as pulses that transfer energy along the axis of propagation.
• Longitudinal waves can be conceptualized as pressure waves characterized by compression and rarefaction.
• rarefaction : a reduction in the density of a material, especially that of a fluid
• Longitudinal : Running in the direction of the long axis of a body.
• compression : to increase in density; the act of compressing, or the state of being compressed; compaction

Longitudinal waves have the same direction of vibration as their direction of travel. This means that the movement of the medium is in the same direction as the motion of the wave. Some longitudinal waves are also called compressional waves or compression waves. An easy experiment for observing longitudinal waves involves taking a Slinky and holding both ends. After compressing and releasing one end of the Slinky (while still holding onto the end), a pulse of more concentrated coils will travel to the end of the Slinky.

Longitudinal Waves : A compressed Slinky is an example of a longitudinal wave. The wave propagates in the same direction of oscillation.

Like transverse waves, longitudinal waves do not displace mass. The difference is that each particle which makes up the medium through which a longitudinal wave propagates oscillates along the axis of propagation. In the example of the Slinky, each coil will oscillate at a point but will not travel the length of the Slinky. It is important to remember that energy, in this case in the form of a pulse, is being transmitted and not the displaced mass.

Longitudinal waves can sometimes also be conceptualized as pressure waves. The most common pressure wave is the sound wave. Sound waves are created by the compression of a medium, usually air. Longitudinal sound waves are waves of alternating pressure deviations from the equilibrium pressure, causing local regions of compression and rarefaction. Matter in the medium is periodically displaced by a sound wave, and thus oscillates. When people make a sound, whether it is through speaking or hitting something, they are compressing the air particles to some significant amount. By doing so, they create transverse waves. When people hear sounds, their ears are sensitive to the pressure differences and interpret the waves as different tones.

Water Waves

Water waves can be commonly observed in daily life, and comprise both transverse and longitudinal wave motion.

Describe particle movement in water waves

• The particles which make up a water wave move in circular paths.
• If the waves move slower than the wind above them, energy is transfered from the wind to the waves.
• The oscillations are greatest on the surface of the wave and become weaker deeper in the fluid.
• phase velocity : The velocity of propagation of a pure sine wave of infinite extent and infinitesimal amplitude.
• group velocity : The propagation velocity of the envelope of a modulated travelling wave, which is considered as the propagation velocity of information or energy contained in it.
• plane wave : A constant-frequency wave whose wavefronts (surfaces of constant phase) are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector.

Water waves, which can be commonly observed in our daily lives, are of specific interest to physicists. Describing detailed fluid dynamics in water waves is beyond the scope of introductory physics courses. Although we often observe water wave propagating in 2D, in this atom we will limit our discussion to 1D propagation.

Water waves : Surface waves in water

The uniqueness of water waves is found in the observation that they comprise both transverse and longitudinal wave motion. As a result, the particles composing the wave move in clockwise circular motion, as seen in. Oscillatory motion is highest at the surface and diminishes exponentially with depth. Waves are generated by wind passing over the surface of the sea. As long as the waves propagate slower than the wind speed just above the waves, there is an energy transfer from the wind to the waves. Both air pressure differences between the upwind and the lee side of a wave crest, as well as friction on the water surface by the wind (making the water to go into the shear stress), contribute to the growth of the waves.

In the case of monochromatic linear plane waves in deep water, particles near the surface move in circular paths, creating a combination of longitudinal (back and forth) and transverse (up and down) wave motions. When waves propagate in shallow water (where the depth is less than half the wavelength ), the particle trajectories are compressed into ellipses. As the wave amplitude (height) increases, the particle paths no longer form closed orbits; rather, after the passage of each crest, particles are displaced slightly from their previous positions, a phenomenon known as Stokes drift.

Plane wave : We see a wave propagating in the direction of the phase velocity. The wave can be thought to be made up of planes orthogonal to the direction of the phase velocity.

Since water waves transport energy, attempts to generate power from them have been made by utilizing the physical motion of such waves. Although larger waves are more powerful, wave power is also determined by wave speed, wavelength, and water density. Deep water corresponds with a water depth larger than half the wavelength, as is a common case in the sea and ocean. In deep water, longer-period waves propagate faster and transport their energy faster. The deep-water group velocity is half the phase velocity. In shallow water for wavelengths larger than about twenty times the water depth (as often found near the coast), the group velocity is equal to the phase velocity. These methods have proven viable in some cases but do not provide a fully sustainable form of renewable energy to date.

Water waves : The motion water waves causes particles to follow clockwise circular motion. This is a result of the wave having both transverse and longitudinal properties.

Wavelength, Freqency in Relation to Speed

Waves are defined by its frequency, wavelength, and amplitude among others. They also have two kinds of velocity: phase and group velocity.

Identify major characteristic properties of waves

• The wavelength is the spatial period of the wave.
• The frequency of a wave refers to the number of cycles per unit time and is not to be confused with angular frequency.
• The phase velocity can be expressed as the product of wavelength and frequency.
• wave speed : The absolute value of the velocity at which the phase of any one frequency component of the wave travels.
• frequency : The quotient of the number of times n a periodic phenomenon occurs over the time t in which it occurs: f = n / t.

Characteristics of Waves

Waves have certain characteristic properties which are observable at first notice. The first property to note is the amplitude. The amplitude is half of the distance measured from crest to trough. We also observe the wavelength, which is the spatial period of the wave (e.g. from crest to crest or trough to trough). We denote the wavelength by the Greek letter [latex]\lambda[/latex].

The frequency of a wave is the number of cycles per unit time — one can think of it as the number of crests which pass a fixed point per unit time. Mathematically, we make the observation that,

Frequencies of different sine waves. : The red wave has a low frequency sine there is very little repetition of cycles. Conversely we say that the purple wave has a high frequency. Note that time increases along the horizontal.

[latex]\begin{equation} \text{f} = \frac{1}{\text{T}} \end{equation}[/latex]

where T is the period of oscillation. Frequency and wavelength can also be related-* with respects to a “speed” of a wave. In fact,

[latex]\begin{equation} \text{v} = \text{f} \lambda \end{equation}[/latex]

where v is called the wave speed, or more commonly,the phase velocity, the rate at which the phase of the wave propagates in space. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity.

Finally, the group velocity of a wave is the velocity with which the overall shape of the waves’ amplitudes — known as the modulation or envelope of the wave — propagates through space. In, one may see that the overall shape (or “envelope”) propagates to the right, while the phase velocity is negative.

Fig 2 : This shows a wave with the group velocity and phase velocity going in different directions. (The group velocity is positive and the phase velocity is negative. )

Energy Transportation

Waves transfer energy which can be used to do work.

Relate direction of energy and wave transportation

• Waves which are more massive transfer more energy.
• Waves with greater velocities transfer more energy.
• Energy of a wave is transported in the direction of the waves transportation.
• energy : A quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent.
• power : A measure of the rate of doing work or transferring energy.
• work : A measure of energy expended in moving an object; most commonly, force times displacement. No work is done if the object does not move.

Energy transportion is essential to waves. It is a common misconception that waves move mass. Waves carry energy along an axis defined to be the direction of propagation. One easy example is to imagine that you are standing in the surf and you are hit by a significantly large wave, and once you are hit you are displaced (unless you hold firmly to your ground!). In this sense the wave has done work (it applied a force over a distance). Since work is done over time, the energy carried by a wave can be used to generate power.

Water Wave : Waves that are more massive or have a greater velocity transport more energy.

Similarly we find that electromagnetic waves carry energy. Electromagnetic radiation (EMR) carries energy—sometimes called radiant energy—through space continuously away from the source (this is not true of the near-field part of the EM field). Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. EMR also carries both momentum and angular momentum. These properties may all be imparted to matter with which it interacts (through work). EMR is produced from other types of energy when created, and it is converted to other types of energy when it is destroyed. The photon is the quantum of the electromagnetic interaction, and is the basic “unit” or constituent of all forms of EMR. The quantum nature of light becomes more apparent at high frequencies (or high photon energy). Such photons behave more like particles than lower-frequency photons do.

Electromagnetic Wave : Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D diagram shows a plane linearly polarized wave propagating from left to right.

In general, there is a relation of waves which states that the velocity ([latex]\text{v}[/latex]) of a wave is proportional to the frequency ([latex]\text{f}[/latex]) times the wavelength ([latex]\lambda[/latex]): [latex]\text{v} = \text{f}\lambda[/latex]

We also know that classical momentum [latex]\text{p}[/latex] is given by [latex]\text{p} = \text{mv}[/latex] which relates to force via Newton’s second law: [latex]\text{F} = \frac{\text{dp}}{\text{dt}}[/latex]

EM waves with higher frequencies carry more energy. This is a direct result of the equations above. Since [latex]\text{v} \propto \text{f}[/latex] we find that higher frequencies imply greater velocity. If velocity is increased then we have greater momentum which implies a greater force (it gets a little bit tricky when we talk about particles moving close to the speed of light, but this observation holds in the classical sense). Since energy is the ability of an object to do work, we find that for [latex]\text{W} = \text{Fd}[/latex] a greater force correlates to more energy transfer. Again, this is an easy phenomenon to experience empirically; just stand in front of a faster wave and feel the difference!

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• Published: 21 October 2021

Determining spatio-temporal characteristics of coseismic travelling ionospheric disturbances (CTID) in near real-time

• Boris Maletckii 1 &
• Elvira Astafyeva 1  

Scientific Reports volume  11 , Article number:  20783 ( 2021 ) Cite this article

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• Natural hazards
• Space physics

Earthquakes are known to generate ionospheric disturbances that are commonly referred to as co-seismic travelling ionospheric disturbances (CTID). In this work, for the first time, we present a novel method that enables to automatically detect CTID in ionospheric GNSS-data, and to determine their spatio-temporal characteristics (velocity and azimuth of propagation) in near-real time (NRT), i.e., less than 15 min after an earthquake. The obtained instantaneous velocities allow us to understand the evolution of CTID and to estimate the location of the CTID source in NRT. Furthermore, also for the first time, we developed a concept of real-time travel-time diagrams that aid to verify the correlation with the source and to estimate additionally the propagation speed of the observed CTID. We apply our methods to the Mw7.4 Sanriku earthquake of 09/03/2011 and the Mw9.0 Tohoku earthquake of 11/03/2011, and we make a NRT analysis of the dynamics of CTID driven by these seismic events. We show that the best results are achieved with high-rate 1 Hz data. While the first tests are made on CTID, our method is also applicable for detection and determining of spatio-temporal characteristics of other travelling ionospheric disturbances that often occur in the ionosphere driven by many geophysical phenomena.

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Introduction

It is known that natural hazard events, such as earthquakes, tsunamis and/or volcanic eruptions generate acoustic and gravity waves that propagate upward in the atmosphere and ionosphere (e.g., 1 , 2 , 3 , 4 , 5 , 6 , 7 ). Earthquake-driven ionospheric disturbances are called co-seismic travelling ionospheric disturbances (CTID). The first CTID are generated directly by the ground or the seafloor via acoustic waves, they reach the ionospheric altitudes (~ 200–350 km) in only 7–9 min. They are followed by acoustic waves generated by the surface Rayleigh waves, and tsunami gravity waves. Nowadays, with the development of permanent networks of dual-frequency Global Navigation Satellite Systems (GNSS) receivers, the detection of CTID and other Natural-Hazard-driven (NH-driven) ionospheric perturbations has nowadays become quite regular (e.g., 5 , 8 , 9 , 10 , 11 , 12 ).

Recently, it has been suggested that NH-driven ionospheric disturbances can be used for more advanced purposes: to localize NH and to estimate the characteristics of the source (e.g., 13 , 14 , 15 , 16 , 17 , 18 , 19 ). Kamogawa et al . 20 suggested a method based on observations of a “tsunami-ionospheric hole”, ionospheric depletion that often occurs after major earthquakes over the epicentral area. Based on the analysis of seven tsunamigenic earthquakes in Japan and Chile, Kamogawa et al . 20 found a quantitative relationship between the initial tsunami height and the TEC depression rate. Manta et al . 21 developed a new ionospheric tsunami power index based on measurements of CTID. They showed that the ionospheric index scales with the volume of water displaced due to an earthquake. However, neither of these methods is real-time compatible. As near-real-time (NRT) mode, we refer to as 10–15 min after an earthquake. Going further towards NRT, Savastano et al . 22 made the first preliminary feasibility demonstration for ionospheric monitoring by GNSS, by developing a software VARION that can derive TEC in NRT. Their technique has been implemented at several GNSS-receivers around the Pacific Ocean ( https://iono2la.gdgps.net ), and is aiming—in the future—to detect traveling ionospheric disturbances (TID) associated with tsunamis. Shrivastava et al . 23 demonstrated the possibility of tsunami detection by GPS-derived TEC, however, no discussion on the real-time use was provided.

Ravanelli et al . 24 claimed to provide the first real-time ionosphere-based tsunami risk assessment by data GNSS receivers in Chile. However, they analyse 2 h of data and used 8th order polynom, i.e., their approach requires stacking of about 2 h of data. Therefore, this approach is not NRT-compatible by our definition.

Therefore, recent seismo-ionospheric results show a big potential for the future use of ionospheric measurements for natural hazard risk assessment. However, before such methods could be applied in real-time, several major developments are yet to be implemented. Going toward real-time applications, the first step is to automatically detect CTID in near-real-time and to analyze their features in order to prove their relation to earthquakes. In this work, we introduce, for the first time, near-real-time compatible methods for determining the spatio-temporal characteristics of CTID.

Estimation of total electron content (TEC) from GNSS

GNSS allows to estimate the ionospheric total electron content (TEC), which is an integral parameter equal to the number of electrons along a line-of-sight (LOS) between a satellite and a receiver. The LOS TEC is often called slant TEC (sTEC). The TEC is usually measured in TEC units (TECU), with 1 TECU equal to 10 16 electrons/m 2 . To calculate the TEC, one needs phase and code measurements performed by dual-frequency receivers (i.e., 25 ). However, the code measurements are only needed to remove the inter-frequency bias. While, the co-seismic signatures and other disturbances can be retrieved from phase TEC estimated solely from phase measurements:

where A  = 40.308 m 3 /s 2 , L 1 and L 2 are phase measurements, λ 1 and λ 2 are wavelengths at the two Global Positioning System (GPS) frequencies (1575,42 and  1227,60 MHz). Therefore, in near-real-time approach, we will only use these phase measurements that can be easily transferred in very short time (Fig.  1 ). The first data point is removed from the whole data series as the unknown bias.

Real-time collection of GNSS phase data and orbit parameters. Networked Transport of RTCM 26 via Internet Protocol (NTRIP) 27 could be used to provide the real-time data stream from  GNSS stations. The main goal of the protocol is Real Time Kinematics (RTK), but it is also suitable for our purposes since it transfers dual-frequency phase and pseudo-range data in real time. RTKLib 28 software could be used to convert binary information from NTRIP data stream. The International GNSS Service (IGS) ultra-rapid orbit 29 is used to obtain the information about the elevation angle and the azimuth. BINEX Binary INdependent EXchange format for files that is used in real-time.

In order to determine the position of ionospheric disturbances, we estimate the coordinates of so-called sub-ionospheric points (SIP) that represent the intersection points between the LOS and the ionospheric thin shell. The satellite orbit information can be rapidly transferred in NRT from the IGS in navigation RINEX files (Fig.  1 ), or it can be forecasted very precisely based on the current known satellite coordinates. Otherwise, ultra-rapid orbits can be used. The shell altitude Hion is not known but presumed from physical principles: we expect the observed perturbation to be concentrated at the altitude of the ionization maximum (HmF2). In NRT, the value of HmF2 can be obtained either from nearest ionosonde stations, or from empirical ionospheric models, such as NeQuick 30 or International Reference Ionosphere (IRI) 31 . Here we take Hion  = 250 km, which is close to the HmF2 on the days of the earthquakes 15 , 32 .

It should be noted that in the vast majority of previous studies of ionospheric response to earthquakes the researchers used band-pass filters, such as running mean, polynomial fitting, high order Butterworth, etc. (e.g., 33 , 34 , 35 ). However, in a real-time scenario one cannot use such filters because of the impossibility to stack long series of data (up to 30–60 min) and due to the lack of time. In addition, the band-pass filtering would induce artefacts and will affect the properties of the detected signals (arrival time, amplitude, spectral components). Therefore, here we suggest to analyze the rate of TEC change (dTEC/dt) instead of the sTEC. Such a derivative procedure works as a high-pass filter and removes the bias and trend caused by the satellite orbit motion. In addition, our dTEC/dt approach will not modify the amplitude of CTID.

Below we use 1 Hz GNSS data for our real-time scenario.

Real-time detection of co-seismic travelling ionospheric disturbances from TEC data series

The concept of the developed method is presented in Fig.  2 . CTID are detected by analysing the sTEC data series by 5-s centered moving averaged over a 5-min window. The averaging prevents detection of random peaks in data. The window duration is chosen to be NRT-compatible and, at the same time, it allows more thorough analysis of CTID characteristics in multiple data series at later steps. Within the selected time window, we search for a local maximum value (LMV) that must exceed every other value within the window.

The concept of the near-real-time detection of CTID and TID, and explanation of the main steps of the procedure.

At step #2, within the window, we switch from sTEC to dTEC/dt. With such an approach, we focus on sudden strong co-seismic TEC signatures that are analogous to the peak ground displacements 36 . Figure  3 a shows examples of CTID detected by GPS stations 0980, 3007 after the 2011 Tohoku-oki earthquake (1 Hz data). The co-seismic signatures in sTEC data series (panels a, b) are quite significant, however, the presence of the trend makes it difficult to calculate the correlation function and the time shift between the data series that are necessary at later steps. In turn, in the dTEC/dt data series, the CTID signatures are visible, but the trend is removed (Fig.  3 c). The chosen 5-min window is enough to compute the correlation, since it catches the CTID signatures and they prevail in the time span.

( a ) Variations of slant TEC registered by GPS satellite 26 at stations 0980 and 3007 following the Tohoku earthquake of 11 March 2011. The earthquake time is indicated by vertical black line. Gray shaded rectangles denote 5-min time window, which is used for further cross-correlation analysis; ( b ) sTEC variations within 5-min time window; ( c ) dTEC/dt within 5-min time window. Black point shows the LMV determined from the sTEC data. The data are 1 Hz; ( d ) Cross-correlation function for the two dTEC/dt time series.

At step #3, we compute the cross-correlation function for two data series in order to obtain the time shifts in the signal arrivals. The latter is found based on the maximum of the cross-correlation function. In addition, the cross-correlation can correct possible errors in finding the LMV. Finally, from the obtained maximum values, it can select 3 GNSS stations for the D1- technique, as explained below in P.3.

To calculate the cross-correlation function, we use Fast Fourier Transformation (FFT), which is a rapid procedure and suitable for NRT applications. Figure  3 d shows an example of the cross-correlation function between dTEC/dt data series at two GPS receivers.

The threshold for the correlated data series depends on the standard deviation of dTEC/dt series:

where \(\sigma_{1} ,\sigma_{2}\) —the standard deviation of dTEC/dt series at GNSS sites. The standard deviation is an indicator of data noisiness. The noisier the data the more difficult it is to detect CTID because of a lower correlation coefficient. Therefore, our approach will adaptively consider the data noise level. Another issue in determining the threshold T is linked with different data cadences. The dTEC/dt values will increase with data cadence. Consequently, to adapt the threshold estimation to different data sampling, we introduce a normalizing coefficient K . For 1-Hz data, the K is chosen to be 10 TECu −1 based on data analysis. Such an adaptive approach makes our method adjustable to the scale of an ionospheric response and aids to automate the triangle selection process (at a later step). It is known that smaller earthquakes generate CTID of smaller amplitudes 51 . When the response is weaker, the threshold is smaller due to the smaller standard deviation of dTEC/dt series and vice versa. (Figure S1 ). Setting a constant threshold may affect the results and that there is a need for an adaptive algorithm for this problem.

Real-time estimation/determining of spatio-temporal parameters: D1-GNSS-RT method

To determine spatio-temporal parameters of CTID, such as the horizontal velocity and the azimuth of propagation, we use a so-called “D1” method. This is an interferometric approach that was introduced by Afraimovich et al . 37 to analyze and detect TID, of which CTID are a subclass. Originally, this method was based on use of GPS-measurements only 37 , 38 . Our method works with all GNSS data, and it is real-time compatible, therefore, we refer to it as “D1-GNSS-RT”.

The disturbances detected by a system of three spatially separated receivers, that act as an interferometric system, are considered to be parts of the same wavefront (Fig.  4 a). Then, by analysing the wave characteristics (such as phase, frequency, signal amplitude) of the observed disturbances, we determine the time shift between CTID arrivals at the detection “triangle”. Three assumptions are used in the subsequent calculations: (1) the wave front is plane, i.e., the distance between the receivers is less than the horizontal dimensions of CTID; (2) the wave front is homogenous; (3) the CTID propagate horizontally i.e. the GNSS-receivers detect the perturbations at the same altitude ( Hion ).

( a ) Explanation of D1 technique . A, B, C—GNSS stations that are used to determine the CSID parameters: horizontal velocity ( v h ) and azimuth ( α ). 0, I, II, III mark the moments of time when the perturbation approaches the detection triangle (0) and when the perturbation is detected at points A, B, and C, respectively. The wavefront is considered to be plain; ( b ) Ionospheric localization of CTIDs based on the known location and values of two velocity vectors V 1 and V 2  as determined by using the D1-method

At the “0” time moment, a disturbance with horizontal velocity v h and azimuth α is approaching the “A–B–C” interferometric system. At the moment “I”, the CTID is detected by the receiver “A”, and it is further moving to other receivers of the system. It is important to note that the consideration of the wave front as plane and homogeneous means that both v h and α would not change when the CTID arrives at the other points of the given system. Garrison et al . 39 showed the correctness of such an assumption for small-scale (3–10 min) TIDs, based on the dense network of receivers in the limited space. At moment “II”, the CTID has already passed receiver “A”, and arrived at receiver “B”. At “III”, the CTID arrives at receiver “C”. Only after this step, one can compute the characteristics of the perturbation. The velocity v h and the azimuth α are then estimated by using the following formulas 40 :

For better spatial representation, the location of the obtained horizontal velocity vector is placed at the point with the first arrival of the disturbance (point A in Fig.  4 a). While, in the temporal domain, the obtained velocity is linked with the arrival time of the disturbance at point C.

As mentioned before, the D1-method is only applicable to a TID with a plain waveform. It is known however that, in most cases, the wave front of CTID is circular (e.g., 5 , 41 ). Therefore, the farther are the stations from one other, the worse is the plain wave condition fulfilled. Also, larger distance between the stations will lower the maximum of the cross-correlation function. Consequently, the D1-GNSS-RT can only be used on a very small segment of the circular wavefront. This limitation requires additional analysis of the positions of the A, B, C receivers with respect to the wavefront. To do that, here we use the cross-correlation function that is the criterion of the similarity of multiple data series. It should be noted that the waveform of the CTID largely depends on the conditions of observations, such as magnetic field configuration in the epicentral area, geometry of GNSS-sounding and the background ionization (e.g., 41 , 42 , 43 , 44 ). Therefore, only perturbations registered close to one another will have similar waveforms.

Localization of the source of ionospheric disturbances

The velocity field obtained by the D1-GNSS-RT method can further be used to locate the source of CTID. The source is defined as a point in the ionosphere where the CTID is generated and starts to propagate horizontally outward from the source. We switch to Latitude–Longitude coordinate system, where x-axis is directed from West to East and y-axis is directed from North to South (Fig.  4 b). We take the azimuths (α i ) and the values (v i ) of the velocities, as well as the coordinates ( \(lon_{0i}\) and \(lat_{0i}\) ) of the velocity “vectors” from the output of the D1-GNSS-RT. This gives us a linear system, where the coordinates ( \(lon_{0}\) and \(lat_{0}\) ) of the source of ionospheric disturbances are unknown. There are two additional restrictions on the system solutions: (1) the horizontal distance between the vectors should be less than 50 km and (2) the difference in the arrival times between points A–B and A–C should be less than 30%. These restrictions are thought to avoid the location of velocity vectors to be on the same segment of the CTID wavefront in order to fulfill the condition of the plain wavefront.

For one velocity vector the distance to the source is defined by the following equation (Fig.  4 b):

where \(lon_{0}\) and \(lat_{0}\) —the coordinates of the source, \(lon_{0i}\) and \(lat_{0i}\) —that of the given velocity vector, α i —the azimuth of the velocity vector. Similarly, for two vectors we obtain:

Based on the system above, the coordinates of the intersection of the two vectors can be estimated as:

Once the source location is known, along with the velocity vector location and its value, the onset time of the source is estimated as follows:

where \(t_{i}\) is the time of the velocity vector and \(\Delta t_{i}\) is defined by:

where \(Dist\left( {lon_{0} , lat_{0} ,lon_{0i} , lat_{0i} } \right)\) is the distance between the source location and the velocity vector location. If the difference in determination of the source onset time from the two given velocities is less than the sampling interval, we consider this pair of velocities as a possible solution for a specific moment of time and location of the source.

We apply our newly developed methods to the cases of two shallow (~ 32 km) earthquakes that occurred in March 2011 off the east coast of Honshu, Japan. The first one is the great M9.1 Tohoku-oki earthquake. According to the US Geological Survey (The National Earthquake Information Center (NEIC); http://earthquake.usgs.gov ), the epicenter of this earthquake was located at 38.322° N and 142.369° E (Fig.  5 a), and the onset time was estimated at 05:46:26 UT. The rupture lasted about 180 s, and caused significant co-seismic cumulative slip with the maximum of 56 m on the north-east from the epicentre (Fig.  5 a) 45 . Several research groups pointed out that the Tohoku earthquake slip consisted of 2 or 3 “segments” (e.g., 46 , 47 ), that present multiple sources for the ionospheric disturbances (e.g., 19 ).

Maps for the Mw9.0 Tohoku earthquake of 11 March 2011 ( a ) and the M7.3 Sanriku earthquake of 9 March 2011 ( b ). Black star shows the epicenter, black dots show GPS receivers, and the colored squares depict the amplitude of the co-seismic slip that occurred due to the earthquakes as calculated by the NEIC USGS 41 . The corresponding color scale is shown on the bottom. The dotted curve shows the position of the Japan Trench. The maps were plotted by using GMT6 software 48 .

The second event is the M7.3 Sanriku-oki earthquake that occurred 55 h before the Tohoku earthquake (i.e., on 9 March) and is often referred to as the Tohoku foreshock. According to the USGS, the rupture started at 02:45:20 UT at the epicentre with coordinates: 38.435° N, 142.842° E (Fig.  5 b). This smaller event lasted 30–40 s and provoked a 2 m co-seismic slip on the north-west from the epicentre (Fig.  5 b) 49 .

To analyze the CTID activity, in both cases, we apply our method to 1 Hz GNSS ionospheric data from the Japan GNSS Earth Observation Network (GEONET, https://www.gsi.go.jp ).

The velocity field and ionospheric localisation of the 2011 M9.1 Tohoku-oki earthquake

The ionospheric response to the Tohoku earthquake was studied in detail by numerous research teams (e.g., 5 , 6 , 14 , 15 , 19 , 50 ). As shown in Fig.  3 , the near-field TEC response showed very complex waveforms, with several peaks in TEC data. The amplitude of this response was also quite significant as compared to other earthquakes and was detected by ten GPS satellites 5 , 6 , 34 , 35 . Here we work with data of GPS satellite 26 that showed the largest and the clearest co-seismic signatures.

The CTID velocity field maps for the first CTID arrivals following the Tohoku earthquake are shown in Fig.  6 a–d, and the localization results are shown in Fig.  6 e–h. It should be noted that, in principle, we can calculate the CTID characteristics for multiple periods of time, as long as the perturbations are detected. For the Tohoku event, instantaneous velocity maps for the first 2 min of CTID detection can be found in Animation S1 (available as supplementary material), and the localization results are shown in Animation S2 (supplementary material). Figure  6 a shows the first velocity vectors at 05:54:13UT, i.e. 487 s after the earthquake onset time, on the north-east from the epicenter. The first vectors are directed south-westward, and the first points have the velocities of about 4 km/s. Such velocity values might correspond to the propagation of the primary (P-) seismic waves (i.e., the rupture propagation), or to the propagation of the Rayleigh surface waves. These first velocity vectors give the first source location at the point with coordinates (38.18; 143.55) (Fig.  6 e). At 05:54:57UT, one can see further development of the CTID evolution within the source area, with smaller velocities. In addition, we notice the occurrence of the second source on the south-east from the epicentre (Fig.  6 b, f). Further, one can clearly see the occurrence of the second segment of the source on the south-east from the epicenter (Fig.  6 d, g). At 05:56:10UT, we observe further evolution of CTID, and westward propagation of CTID with velocities from 600 m/s to ~ 3 km/s. This range of velocities was previously observed for the CTID generated by the Tohoku earthquake (e.g., 5 , 6 , 14 ).

( a-d) CTID velocity field calculated from the first CTID detected by GPS satellite PRN 26 after the Tohoku earthquake. The dotted curve shows the position of the Japan Trench, black star depicts the epicenter. The gray arrow corresponds to 1.1 km/s; (e–h) localization of the seismic source as estimated from the first velocity vectors shown on panels (a–d).

The CTID propagation speed can be verified by plotting so-called travel-time diagrams (TTD), that present 3-D diagrams with the distance from the source versus time after the source onset, and the amplitude of CTID is shown in color. TTD also enable to confirm the correlation of the observed perturbations with the source. In retrospective studies, a band-pass filter was applied in order to better extract the co-seismic signatures and to clearly see the correlation with the source. In NRT mode, and with the impossibility to use such a filter, we suggest using dTEC/dt parameter, and we call such diagrams near-real-time TTD (NRT-TTD). This is the first NRT-compatible method proposed for obtaining the TTD. As a source, at the first approximation, we can take the epicentre position that should be known from seismological data several minutes after the earthquake. However, the epicentre is the point where the rupture starts, and its position does not always correspond (especially for large earthquakes) to the position of the co-seismic crustal uplift that generates CTID as well as tsunamis. The problem lies, however, in the fact that in NRT, it is very difficult to know the position of the uplift or the slip. Therefore, we can take the position of the source estimated from our ionospheric methods.

The NRT-TTD for the Tohoku event, G26 satellite, plotted for the source located at the epicentre, the center of the maximum slip (38.64; 143.35) and the “ionospheric source” (37.944; 143.153) are presented in Fig.  7 a–c, respectively. It should be noted that the Tohoku earthquake produced significant displacement of the ground on a large area (the approximative fault size is about 300*80 km) and, strictly speaking, taking a single point as the source is an approximation. However, we proceed with such an assumption to plot the NRT-TTD. The correlation is seen when CTID propagates “linearly” from the source. Comparison of Fig.  7 a–c reveals that the best correlation is obtained for the slip maximum (Fig.  7 b) and for the ionospherically-determined source (Fig.  7 c). While, the perturbation is not well-aligned when the diagram is plotted with respect to the epicentre (Fig.  7 a). The propagation speed of the observed CTID can be estimated from the slopes on the TTD. We find the speeds to be ~ 2.3–2.6 km/s, which is in line with previous retrospective observations for the ionospheric response to the Tohoku earthquake (e.g., 5 , 6 , 14 , 15 ).

Near-real-time travel time diagram (NRT-TTD) plotted by using dTEC/dt data for the Tohoku ( a – c ) earthquake (satellite G26) and Sanriku ( d – f ) earthquake (satellite G07). In panels ( a , d ) the distance is calculated with respect to the earthquakes’ epicenters as estimated by the USGS, in panels ( b , e )—with respect to the maximum co-seismic uplifts; ( c , f )—with respect to the ionospheric localization as shown in Fig.  5 d, e and 6 d, e. The color scale is shown on the right.

The velocity field and ionospheric localisation of the 2011 M7.3 Sanriku-oki earthquake

Ionospheric response to the Sanriku earthquake was studied previously by Thomas et al . 53 and Astafyeva and Shults 32 . The co-seismic TEC signatures were detected by satellites G07 and G10. Here we only focus on CTID registered by GPS satellite G07. Contrary to the CTID generated by the Mw9.0 Tohoku earthquake, the ionospheric TEC response to this smaller earthquake presented the commonly known N-wave signatures with smaller amplitudes. However, even despite the smaller amplitude of CTID, our method detects these disturbances.

The instantaneous velocity field maps are presented in Fig.  8 a–d. One can notice that the picture of the velocity field for the CTID generated by the Sanriku event is much simpler that the one for the Tohoku event. The first velocity vector is shown at 02:55:08UT, i.e. 588 s after the earthquake onset time. At that instant, the CTID starts to propagate south-westward at the velocity of about 850 m/s (Fig.  8 a). Within the next minute, we observe south-westward propagation of ionospheric disturbances at ~ 850–1100 m/s (Fig.  8 b, c). At 02:56:08UT, we observe further southwestward propagation of CTID (Fig.  8 d). From these first velocity fields, we estimate the location of the source to be on the south-east from the epicentre (Fig.  8 e–h). Overall, one can notice significant difference in the velocity field and CTID evolution during this smaller earthquake. The CTID have lower velocities, and the velocity field is much less complex as compared to the Tohoku earthquake.

( a – d ) CTID velocity field calculated from the first CTID detected by GPS satellite PRN 07 following the Sanriku earthquake. The dotted curve shows the position of the Japan Trench, black star depicts the epicenter. The gray arrow corresponds to 1.1 km/s; ( e – h ) localization of the seismic source as estimated from the first velocity vectors shown on panels ( a – d ).

The corresponding RT-TTD calculated with respect to the epicentre, the maximum slip point (38.5; 142.7), and the ionospherically determined (38.335; 143.442) source are presented in Fig.  7 d–f, respectively. The best alignment is achieved for the ionospheric source (Fig.  7 e), where we also see concurrent northward and southward propagation from the source. While, for the two other sources one cannot clearly see this effect (Fig.  7 a, e). Therefore, our results suggest that the source was located on the south-east from the epicentre. The worst alignment is obtained for the epicentre as the source of CTID (Fig.  7 d). The CTID propagation speed is estimated to be 1.2–1.6 km/s, which is close to the estimation in after-earthquake analysis by Astafyeva and Shults 32 .

Discussions

Above we demonstrated the possibility to calculate in NRT spatio-temporal characteristics of CTID on the example of two earthquake events that occurred in Japan in March 2011. For both earthquakes, we also localized in NRT the source of the observed CTIDs. It should be reminded that the CTID coordinates and, consequently, the estimated position of ionospheric sources will change if we vary the altitude of detection Hion . In this work, we took Hion  = 250 km, which is close to the ionization maximum in the epicentral areas during the earthquakes, and is the right choice from a physical point of view. However, recently it has been suggested that the actual GNSS detection of CTID may take place at lower altitudes 19 , 32 , 53 . Therefore, strictly speaking, the Hion should be determined each time for the correct estimation of the CTID coordinates. Our method is fully operational independently on the Hion value, however, its results and the accuracy of the ionospheric source localization might be improved if/when we know the real Hion . Determining the exact altitude of detection is out of the scope of the current work.

Here we used 1 Hz GNSS TEC data from the Japanese network of GPS receivers GEONET, i.e. a network with good spatial coverage with 20-km distance between the receivers, and we demonstrated that in such observational conditions, our NRT-compatible methods provide good results both in terms of the source localisation and determining of CTID spatio-temporal characteristics. In our method, the accuracy of localisation seems lower than that by seismic stations that invert the position of the epicentre based on detection of seismic waves. The seismic source can also be localized by other non-seismic instrumentation, such as by balloon pressure sensors via detection of infrasound signals due to earthquakes. For instance, Krishnamoorthy et al . 54 showed that the source can be localized with 90% probability within an ellipse with a semimajor axis approximately 80 m under the perfect conditions. They used 26 shots that is equal to the usage of a 26-balloon array to solve this task. It should be noted, however, that this result was obtained by a-posteriori analysis, therefore it might be quite challenging to repeat such quality in NRT.

Further, we discuss how lower or much lower spatial and temporal resolutions of GNSS ionospheric data could affect the output of our methods. Also, the accuracy of estimation of the velocities and the source location should be determined.

With regards to the data sampling, for both earthquakes, we tested our methods on 30-s data that are available from the GSI ( http://datahouse1.gsi.go.jp/terras/terras_english.html ). We have found that such a resolution is not enough because of two main reasons. First, fewer data within the selected window duration of 5 min will smooth the dTEC/dt values, which, in turn, will erase the specific features of CTID that characterize different segments of the wavefront. As mentioned before, the D1-GNSS-RT method can only be used on a small part of a wavefront, because it is only applicable to the plain wave. Therefore, with 30-s data sampling, it is difficult to control this condition in terms of the correlation between data series, especially for smaller earthquakes, for which the response is smaller in amplitude and duration 51 . Second, 30-s data rate will introduce ± 15-s error in the LMV determining within the window, and, consequently, it will lead to errors in the arrival time at each point of a triangle. The impact of such ± 15-s error can be seen in Fig.  9 a, b, where we present the normalized number of the time shifts between points A–B (red, ΔT 1 ) and A–C (blue, ΔT 2 ) of a triangle for the Tohoku (a) and Sanriku (b) earthquakes. For both events, the distribution of ΔT 1 and ΔT 2 have the same shape and look quite similar, but are shifted for ~ 5 s. This emphasizes the fact that a CTID arrives at points B and C at close moments of time, that is only possible if the arrivals belong to the same segment on a circular disturbance wavefront. One can also notice that, for both events, the majority of arrivals are registered within a narrow period of time, 20–40 s for the Sanriku event (Fig.  9 a) and 25–60 s for the Tohoku event (Fig.  9 b). This means that lower time steps in data will lead to errors in the correct detection of the moment of arrival would occur, and, consequently will eventually impact the velocity values and the azimuths.

To further analyze the applicability of our method to lower cadence data, we downsampled the initial 1 Hz data to 5-, 10- and 15-s cadence. Figure  10 shows how different data cadences impact the distribution of calculated velocities. One can see a significant difference in the results for 1 s and 30 s data. Therefore, for better performance of our methods we suggest the use of GNSS-data with 1 Hz sampling.

( a – b ) Distribution of normalized number of the time shifts between points A–B (red, ΔT 1 ) and A–C (blue, ΔT 2 ) of a triangle for the Tohoku ( a ) and Sanriku ( b ) earthquakes; ( c ) impact of an error of ± 0.5 s on arrival times affects the computation of the velocities values and azimuths.

Distribution of velocity values calculated from data of different temporal cadences: 1-(red), 5-(green), 10-(blue), 15-(gray), 30-(brown) seconds.

With respect to the accuracy of our method, we analyzed how an error of ± 0.5 s in arrival times affects the computation of the velocity values and azimuths. The normalized number of error cases versus the absolute error percentage is shown in Fig.  9 c. One can see that ~ 80% of both velocities and azimuths have less than 2.5% of errors and ~ 95%—less than 5%. These results also confirm the advantage of high-rate data.

The use of different orbital information can impact the accuracy of our method, because the coordinates of CTID depend on the position of a satellite as well as of that of a GNSS station. The commonly used ephemerides are those transferred in the RINEX navigation file. Alternatively, ultra-rapid orbits can be used. We compared the amplitude and direction of the obtained velocity vectors based on ultra-rapid orbits with those calculated based on the use of the RINEX navigation files (Fig.  11 a, b). Then, we computed source locations based on these velocities and estimated the error in position (Fig.  11 c, d). This analysis was made both for the Tohoku and the Sanriku cases. One can see that the majority of both velocities and azimuths have less than 0.05% of differences. This fact can be explained by the high quality (cm-accuracy) of the real-time IGS products 55 . However, the radar diagrams of error positioning show worse results (Fig.  11 c, d).

Accuracy comparison based on different sources of the orbits: navigational RINEX file and ultra-rapid orbits. Panel ( a )—distribution of percentage difference of amplitude and azimuth of propagation for the Tohoku case (y-axis logarithmic scale); panel ( b )—distribution of percentage difference of amplitude and azimuth of propagation for the Sanriku case (y-axis logarithmic scale); panel ( c )—radar diagram of source location difference for the Tohoku case; panel ( d )—radar diagram of source location difference for the Sanriku case.

Finally, we would like to note that our methods can be used for detection of TID of other origins in addition to CTID and, therefore, it is useful for real-time Space Weather applications. The D1-GNSS-RT will automatically catch all CTID and TID with high dTEC/dt values, where the maximum disturbance amplitude exceeds the noise level by at least 4 times (Figure S4 a). Such disturbances could be generated by acoustic or gravito-acoustic waves (earthquakes, volcanic eruptions, rocket launches), or by enhanced EUV radiation (solar flares) that produces rapid growth of the ionization in the ionosphere (Fig.  12 ). It should be emphasized that for the detection, the absolute amplitude of CTID and TID is less important than the dTEC/dt. For instance, it is known that smaller earthquakes generate smaller disturbances in the ionosphere 51 , 52 . Therefore, it is of interest to apply our technique to the smallest earthquake ever recorded in the ionosphere—the M6.6 16 July 2007 Chuetsu earthquake in Japan 52 . The Chuetsu earthquake produced a very small-amplitude TEC disturbance that was registered by satellite G26 and by a few GPS-stations in the near-epicentral region, and the only data available were of 30-s cadence. Unfortunately, the latter factors did not allow us to compute the velocities and the localization by using the D1-GNSS-RT technique. However, our method successfully found the LMV even for such small CTID but with sufficient dTEC/dt rate (Figure S5 b, c). Also, Figure S5 demonstrates that we could track the CTID propagation with respect to the source in NRT by using our RT-TTD technique.

Examples of TEC disturbances of different origin that are detectable by our approach. Panel ( a )—slant TEC values characterized by high changes, panel ( b ) — rate of TEC of the exact data series.

On the other hand, disturbances with lower sTEC derivative or/and higher noise level might appear undetectable or the D1 triangles will not be formed because of low cross-correlation between data series. For instance, we did not manage to catch CTID registered by satellites G27 (during the Tohoku earthquake) and G10 (during the Sanriku earthquake), because they had low dTEC/dt. Another example is the ionospheric response to the M7.8 2016 Kaikoura earthquake that occurred on 13 November 2016 in New Zealand, for which we also analysed high-rate 1 Hz data. The latter TEC variations presented more noise and the amplitude of the detected CTID did not grow up as fast as for the Tohoku and Sanriku cases (Figure S4 ). For such less pronounced disturbances, other more sophisticated methods should be developed, which is a subject of a future separate work.

Conclusions

For the first time, we introduce a NRT-compatible method that allows very rapid determining of spatio-temporal parameters of travelling ionospheric disturbances. By using our method, one can obtain instantaneous velocity maps for ionospheric perturbations, and to estimate the position of the source. In addition, also for the first time, we present real-time travel-time diagrams. We demonstrate the performance of our methods on CTID generated by the Tohoku-oki Earthquake of 11 March 2011 and the Sanriku-oki Earthquake of 9 March 2011. We use high-rate 1 Hz GPS data from the Japan network GEONET for these two earthquakes, and we observe the evolution of the CTID over the source area as it could have been seen in real-time. We show that there is a significant difference between CTID generated by M9 and M7.3 earthquakes in terms of CTID velocities and evolution: the giant Tohoku earthquake generated a massive TEC response in both amplitude and spatial extent, and such a difference can be clearly seen in our results.

It is important to emphasize that, besides CTID, our method can detect and analyze other TID that often occur and propagate in the ionosphere. Therefore, the D1-GNSS-RT method can be used for near-real-time Space Weather applications.

Data availability

The data are available from the GeoSpatial Authority of Japan (GSI, terras.go.jp). http://datahouse1.gsi.go.jp/terras/terras_english.html .

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Thomas, D. et al. Revelation of early detection of co-seismic ionospheric perturbations in GPS-TEC from realistic modelling approach: Case study. Sci. Rep. 8 , 12105. https://doi.org/10.1038/s41598-018-30476-9 (2018).

Krishnamoorthy, S. et al. Aerial seismology using balloon-based barometers. IEEE Trans. Geosci. Remote Sens. 57 (12), 10191–10201. https://doi.org/10.1109/TGRS.2019.2931831 (2019).

Hadas, T. & Bosy, J. IGS RTS precise orbits and clocks verification and quality degradation over time. GPS Solut. 19 , 93–105. https://doi.org/10.1007/s10291-014-0369-5 (2015).

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Acknowledgements

We thank the French Space Agency (CNES, Project “IMAGION”) for the support. BM additionally thanks the CNES and the IPGP for the Ph.D. fellowship and the support of the RFBR, Grant No. 19-05-00889, and partly by budgetary funding of Basic Research Program II.16. This is IPGP contribution 4241.

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Maletckii, B., Astafyeva, E. Determining spatio-temporal characteristics of coseismic travelling ionospheric disturbances (CTID) in near real-time. Sci Rep 11 , 20783 (2021). https://doi.org/10.1038/s41598-021-99906-5

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disturbance

Definition of disturbance

• alarums and excursions
• clutter [ chiefly dialect ]
• corroboree [ Australian ]
• do [ chiefly dialect ]
• helter-skelter
• hoo-hah
• hubble-bubble
• hurly-burly
• hurry-scurry
• hurry-skurry
• kerfuffle [ chiefly British ]
• pandemonium
• splore [ Scottish ]

Examples of disturbance in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'disturbance.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

13th century, in the meaning defined at sense 1

Phrases Containing disturbance

• disturbance of the peace

Dictionary Entries Near disturbance

Cite this entry.

“Disturbance.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/disturbance. Accessed 5 Apr. 2024.

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Middle school physics - NGSS

Course: middle school physics - ngss   >   unit 4, mechanical waves and light.

• Understand: mechanical waves and light

Key points:

• Sound waves, water waves, and seismic waves are all types of mechanical waves.
• Light is a form of electromagnetic wave.
• A light wave’s amplitude determines how intense, or bright, it is. Its frequency determines the light wave’s color.
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16.1 Traveling Waves

Learning objectives.

By the end of this section, you will be able to:

• Describe the basic characteristics of wave motion
• Define the terms wavelength, amplitude, period, frequency, and wave speed
• Explain the difference between longitudinal and transverse waves, and give examples of each type
• List the different types of waves

We saw in Oscillations that oscillatory motion is an important type of behavior that can be used to model a wide range of physical phenomena. Oscillatory motion is also important because oscillations can generate waves, which are of fundamental importance in physics. Many of the terms and equations we studied in the chapter on oscillations apply equally well to wave motion ( Figure ).

Types of Waves

A wave is a disturbance that propagates, or moves from the place it was created. There are three basic types of waves: mechanical waves, electromagnetic waves, and matter waves.

Basic mechanical waves are governed by Newton’s laws and require a medium. A medium is the substance a mechanical waves propagates through, and the medium produces an elastic restoring force when it is deformed. Mechanical waves transfer energy and momentum, without transferring mass. Some examples of mechanical waves are water waves, sound waves, and seismic waves. The medium for water waves is water; for sound waves, the medium is usually air. (Sound waves can travel in other media as well; we will look at that in more detail in Sound .) For surface water waves, the disturbance occurs on the surface of the water, perhaps created by a rock thrown into a pond or by a swimmer splashing the surface repeatedly. For sound waves, the disturbance is a change in air pressure, perhaps created by the oscillating cone inside a speaker or a vibrating tuning fork. In both cases, the disturbance is the oscillation of the molecules of the fluid. In mechanical waves, energy and momentum transfer with the motion of the wave, whereas the mass oscillates around an equilibrium point. (We discuss this in Energy and Power of a Wave .) Earthquakes generate seismic waves from several types of disturbances, including the disturbance of Earth’s surface and pressure disturbances under the surface. Seismic waves travel through the solids and liquids that form Earth. In this chapter, we focus on mechanical waves.

Electromagnetic waves are associated with oscillations in electric and magnetic fields and do not require a medium. Examples include gamma rays, X-rays, ultraviolet waves, visible light, infrared waves, microwaves, and radio waves. Electromagnetic waves can travel through a vacuum at the speed of light, [latex]v=c=2.99792458\times {10}^{8}\,\text{m/s}.[/latex] For example, light from distant stars travels through the vacuum of space and reaches Earth. Electromagnetic waves have some characteristics that are similar to mechanical waves; they are covered in more detail in Electromagnetic Waves in volume 2 of this text.

Matter waves are a central part of the branch of physics known as quantum mechanics. These waves are associated with protons, electrons, neutrons, and other fundamental particles found in nature. The theory that all types of matter have wave-like properties was first proposed by Louis de Broglie in 1924. Matter waves are discussed in Photons and Matter Waves in the third volume of this text.

Mechanical Waves

Mechanical waves exhibit characteristics common to all waves, such as amplitude, wavelength, period, frequency, and energy. All wave characteristics can be described by a small set of underlying principles.

The simplest mechanical waves repeat themselves for several cycles and are associated with simple harmonic motion. These simple harmonic waves can be modeled using some combination of sine and cosine functions. For example, consider the simplified surface water wave that moves across the surface of water as illustrated in Figure . Unlike complex ocean waves, in surface water waves, the medium, in this case water, moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. In Figure , the waves causes a seagull to move up and down in simple harmonic motion as the wave crests and troughs (peaks and valleys) pass under the bird. The crest is the highest point of the wave, and the trough is the lowest part of the wave. The time for one complete oscillation of the up-and-down motion is the wave’s period T . The wave’s frequency is the number of waves that pass through a point per unit time and is equal to [latex]f=1\text{/}T.[/latex] The period can be expressed using any convenient unit of time but is usually measured in seconds; frequency is usually measured in hertz (Hz), where [latex]1\,{\text{Hz}=1\,\text{s}}^{-1}.[/latex]

The length of the wave is called the wavelength and is represented by the Greek letter lambda [latex](\lambda )[/latex], which is measured in any convenient unit of length, such as a centimeter or meter. The wavelength can be measured between any two similar points along the medium that have the same height and the same slope. In Figure , the wavelength is shown measured between two crests. As stated above, the period of the wave is equal to the time for one oscillation, but it is also equal to the time for one wavelength to pass through a point along the wave’s path.

The amplitude of the wave ( A ) is a measure of the maximum displacement of the medium from its equilibrium position. In the figure, the equilibrium position is indicated by the dotted line, which is the height of the water if there were no waves moving through it. In this case, the wave is symmetrical, the crest of the wave is a distance [latex]\text{+}A[/latex] above the equilibrium position, and the trough is a distance [latex]\text{−}A[/latex] below the equilibrium position. The units for the amplitude can be centimeters or meters, or any convenient unit of distance.

The water wave in the figure moves through the medium with a propagation velocity [latex]\mathbf{\overset{\to }{v}}.[/latex] The magnitude of the wave velocity is the distance the wave travels in a given time, which is one wavelength in the time of one period, and the wave speed is the magnitude of wave velocity. In equation form, this is

This fundamental relationship holds for all types of waves. For water waves, v is the speed of a surface wave; for sound, v is the speed of sound; and for visible light, v is the speed of light.

Transverse and Longitudinal Waves

We have seen that a simple mechanical wave consists of a periodic disturbance that propagates from one place to another through a medium. In Figure (a), the wave propagates in the horizontal direction, whereas the medium is disturbed in the vertical direction. Such a wave is called a transverse wave . In a transverse wave, the wave may propagate in any direction, but the disturbance of the medium is perpendicular to the direction of propagation. In contrast, in a longitudinal wave or compressional wave, the disturbance is parallel to the direction of propagation. Figure (b) shows an example of a longitudinal wave. The size of the disturbance is its amplitude A and is completely independent of the speed of propagation v .

A simple graphical representation of a section of the spring shown in Figure (b) is shown in Figure . Figure (a) shows the equilibrium position of the spring before any waves move down it. A point on the spring is marked with a blue dot. Figure (b) through (g) show snapshots of the spring taken one-quarter of a period apart, sometime after the end of` the spring is oscillated back and forth in the x -direction at a constant frequency. The disturbance of the wave is seen as the compressions and the expansions of the spring. Note that the blue dot oscillates around its equilibrium position a distance A , as the longitudinal wave moves in the positive x -direction with a constant speed. The distance A is the amplitude of the wave. The y -position of the dot does not change as the wave moves through the spring. The wavelength of the wave is measured in part (d). The wavelength depends on the speed of the wave and the frequency of the driving force.

Waves may be transverse, longitudinal, or a combination of the two. Examples of transverse waves are the waves on stringed instruments or surface waves on water, such as ripples moving on a pond. Sound waves in air and water are longitudinal. With sound waves, the disturbances are periodic variations in pressure that are transmitted in fluids. Fluids do not have appreciable shear strength, and for this reason, the sound waves in them are longitudinal waves. Sound in solids can have both longitudinal and transverse components, such as those in a seismic wave. Earthquakes generate seismic waves under Earth’s surface with both longitudinal and transverse components (called compressional or P-waves and shear or S-waves, respectively). The components of seismic waves have important individual characteristics—they propagate at different speeds, for example. Earthquakes also have surface waves that are similar to surface waves on water. Ocean waves also have both transverse and longitudinal components.

Wave on a String

A student takes a 30.00-m-long string and attaches one end to the wall in the physics lab. The student then holds the free end of the rope, keeping the tension constant in the rope. The student then begins to send waves down the string by moving the end of the string up and down with a frequency of 2.00 Hz. The maximum displacement of the end of the string is 20.00 cm. The first wave hits the lab wall 6.00 s after it was created. (a) What is the speed of the wave? (b) What is the period of the wave? (c) What is the wavelength of the wave?

• The speed of the wave can be derived by dividing the distance traveled by the time.
• The period of the wave is the inverse of the frequency of the driving force.
• The wavelength can be found from the speed and the period [latex]v=\lambda \text{/}T.[/latex]
• The first wave traveled 30.00 m in 6.00 s: [latex]v=\frac{30.00\,\text{m}}{6.00\,\text{s}}=5.00\frac{\text{m}}{\text{s}}.[/latex]
• The period is equal to the inverse of the frequency: [latex]T=\frac{1}{f}=\frac{1}{2.00\,{\text{s}}^{-1}}=0.50\,\text{s}.[/latex]
• The wavelength is equal to the velocity times the period: [latex]\lambda =vT=5.00\frac{\text{m}}{\text{s}}(0.50\,\text{s})=2.50\,\text{m}.[/latex]

Significance

The frequency of the wave produced by an oscillating driving force is equal to the frequency of the driving force.

Check Your Understanding

When a guitar string is plucked, the guitar string oscillates as a result of waves moving through the string. The vibrations of the string cause the air molecules to oscillate, forming sound waves. The frequency of the sound waves is equal to the frequency of the vibrating string. Is the wavelength of the sound wave always equal to the wavelength of the waves on the string?

The wavelength of the waves depends on the frequency and the velocity of the wave. The frequency of the sound wave is equal to the frequency of the wave on the string. The wavelengths of the sound waves and the waves on the string are equal only if the velocities of the waves are the same, which is not always the case. If the speed of the sound wave is different from the speed of the wave on the string, the wavelengths are different. This velocity of sound waves will be discussed in Sound .

Characteristics of a Wave

A transverse mechanical wave propagates in the positive x -direction through a spring (as shown in Figure (a)) with a constant wave speed, and the medium oscillates between [latex]\text{+}A[/latex] and [latex]\text{−}A[/latex] around an equilibrium position. The graph in Figure shows the height of the spring ( y ) versus the position ( x ), where the x -axis points in the direction of propagation. The figure shows the height of the spring versus the x -position at [latex]t=0.00\,\text{s}[/latex] as a dotted line and the wave at [latex]t=3.00\,\text{s}[/latex] as a solid line. (a) Determine the wavelength and amplitude of the wave. (b) Find the propagation velocity of the wave. (c) Calculate the period and frequency of the wave.

• The amplitude and wavelength can be determined from the graph.
• Since the velocity is constant, the velocity of the wave can be found by dividing the distance traveled by the wave by the time it took the wave to travel the distance.
• The period can be found from [latex]v=\frac{\lambda }{T}[/latex] and the frequency from [latex]f=\frac{1}{T}.[/latex]

• The distance the wave traveled from time [latex]t=0.00\,\text{s}[/latex] to time [latex]t=3.00\,\text{s}[/latex] can be seen in the graph. Consider the red arrow, which shows the distance the crest has moved in 3 s. The distance is [latex]8.00\,\text{cm}-2.00\,\text{cm}=6.00\,\text{cm}.[/latex] The velocity is [latex]v=\frac{\Delta x}{\Delta t}=\frac{8.00\,\text{cm}-2.00\,\text{cm}}{3.00\,\text{s}-0.00\,\text{s}}=2.00\,\text{cm/s}.[/latex]
• The period is [latex]T=\frac{\lambda }{v}=\frac{8.00\,\text{cm}}{2.00\,\text{cm/s}}=4.00\,\text{s}[/latex] and the frequency is [latex]f=\frac{1}{T}=\frac{1}{4.00\,\text{s}}=0.25\,\text{Hz}.[/latex]

Note that the wavelength can be found using any two successive identical points that repeat, having the same height and slope. You should choose two points that are most convenient. The displacement can also be found using any convenient point.

The propagation velocity of a transverse or longitudinal mechanical wave may be constant as the wave disturbance moves through the medium. Consider a transverse mechanical wave: Is the velocity of the medium also constant?

• A wave is a disturbance that moves from the point of origin with a wave velocity v .
• A wave has a wavelength [latex]\lambda[/latex], which is the distance between adjacent identical parts of the wave. Wave velocity and wavelength are related to the wave’s frequency and period by [latex]v=\frac{\lambda }{T}=\lambda f.[/latex]
• Mechanical waves are disturbances that move through a medium and are governed by Newton’s laws.
• Electromagnetic waves are disturbances in the electric and magnetic fields, and do not require a medium.
• Matter waves are a central part of quantum mechanics and are associated with protons, electrons, neutrons, and other fundamental particles found in nature.
• A transverse wave has a disturbance perpendicular to the wave’s direction of propagation, whereas a longitudinal wave has a disturbance parallel to its direction of propagation.

Conceptual Questions

Give one example of a transverse wave and one example of a longitudinal wave, being careful to note the relative directions of the disturbance and wave propagation in each.

A sinusoidal transverse wave has a wavelength of 2.80 m. It takes 0.10 s for a portion of the string at a position x to move from a maximum position of [latex]y=0.03\,\text{m}[/latex] to the equilibrium position [latex]y=0.[/latex] What are the period, frequency, and wave speed of the wave?

What is the difference between propagation speed and the frequency of a mechanical wave? Does one or both affect wavelength? If so, how?

Propagation speed is the speed of the wave propagating through the medium. If the wave speed is constant, the speed can be found by [latex]v=\frac{\lambda }{T}=\lambda f.[/latex] The frequency is the number of wave that pass a point per unit time. The wavelength is directly proportional to the wave speed and inversely proportional to the frequency.

Consider a stretched spring, such as a slinky. The stretched spring can support longitudinal waves and transverse waves. How can you produce transverse waves on the spring? How can you produce longitudinal waves on the spring?

Consider a wave produced on a stretched spring by holding one end and shaking it up and down. Does the wavelength depend on the distance you move your hand up and down?

No, the distance you move your hand up and down will determine the amplitude of the wave. The wavelength will depend on the frequency you move your hand up and down, and the speed of the wave through the spring.

A sinusoidal, transverse wave is produced on a stretched spring, having a period T . Each section of the spring moves perpendicular to the direction of propagation of the wave, in simple harmonic motion with an amplitude A . Does each section oscillate with the same period as the wave or a different period? If the amplitude of the transverse wave were doubled but the period stays the same, would your answer be the same?

An electromagnetic wave, such as light, does not require a medium. Can you think of an example that would support this claim?

Storms in the South Pacific can create waves that travel all the way to the California coast, 12,000 km away. How long does it take them to travel this distance if they travel at 15.0 m/s?

Waves on a swimming pool propagate at 0.75 m/s. You splash the water at one end of the pool and observe the wave go to the opposite end, reflect, and return in 30.00 s. How far away is the other end of the pool?

[latex]2d=vt\Rightarrow d=11.25\,\text{m}[/latex]

Wind gusts create ripples on the ocean that have a wavelength of 5.00 cm and propagate at 2.00 m/s. What is their frequency?

How many times a minute does a boat bob up and down on ocean waves that have a wavelength of 40.0 m and a propagation speed of 5.00 m/s?

Scouts at a camp shake the rope bridge they have just crossed and observe the wave crests to be 8.00 m apart. If they shake the bridge twice per second, what is the propagation speed of the waves?

What is the wavelength of the waves you create in a swimming pool if you splash your hand at a rate of 2.00 Hz and the waves propagate at a wave speed of 0.800 m/s?

[latex]v=f\lambda \Rightarrow \lambda =0.400\,\text{m}[/latex]

What is the wavelength of an earthquake that shakes you with a frequency of 10.0 Hz and gets to another city 84.0 km away in 12.0 s?

Radio waves transmitted through empty space at the speed of light [latex](v=c=3.00\times {10}^{8}\,\text{m/s})[/latex] by the Voyager spacecraft have a wavelength of 0.120 m. What is their frequency?

Your ear is capable of differentiating sounds that arrive at each ear just 0.34 ms apart, which is useful in determining where low frequency sound is originating from. (a) Suppose a low-frequency sound source is placed to the right of a person, whose ears are approximately 18 cm apart, and the speed of sound generated is 340 m/s. How long is the interval between when the sound arrives at the right ear and the sound arrives at the left ear? (b) Assume the same person was scuba diving and a low-frequency sound source was to the right of the scuba diver. How long is the interval between when the sound arrives at the right ear and the sound arrives at the left ear, if the speed of sound in water is 1500 m/s? (c) What is significant about the time interval of the two situations?

(a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the distance to the epicenter of the quake, geologists compare the arrival times of S- and P-waves, which travel at different speeds. If S- and P-waves travel at 4.00 and 7.20 km/s, respectively, in the region considered, how precisely can the distance to the source of the earthquake be determined? (b) Seismic waves from underground detonations of nuclear bombs can be used to locate the test site and detect violations of test bans. Discuss whether your answer to (a) implies a serious limit to such detection. (Note also that the uncertainty is greater if there is an uncertainty in the propagation speeds of the S- and P-waves.)

a. The P-waves outrun the S-waves by a speed of [latex]v=3.20\,\text{km/s;}[/latex] therefore, [latex]\Delta d=0.320\,\text{km}.[/latex] b. Since the uncertainty in the distance is less than a kilometer, our answer to part (a) does not seem to limit the detection of nuclear bomb detonations. However, if the velocities are uncertain, then the uncertainty in the distance would increase and could then make it difficult to identify the source of the seismic waves.

A Girl Scout is taking a 10.00-km hike to earn a merit badge. While on the hike, she sees a cliff some distance away. She wishes to estimate the time required to walk to the cliff. She knows that the speed of sound is approximately 343 meters per second. She yells and finds that the echo returns after approximately 2.00 seconds. If she can hike 1.00 km in 10 minutes, how long would it take her to reach the cliff?

A quality assurance engineer at a frying pan company is asked to qualify a new line of nonstick-coated frying pans. The coating needs to be 1.00 mm thick. One method to test the thickness is for the engineer to pick a percentage of the pans manufactured, strip off the coating, and measure the thickness using a micrometer. This method is a destructive testing method. Instead, the engineer decides that every frying pan will be tested using a nondestructive method. An ultrasonic transducer is used that produces sound waves with a frequency of [latex]f=25\,\text{kHz}.[/latex] The sound waves are sent through the coating and are reflected by the interface between the coating and the metal pan, and the time is recorded. The wavelength of the ultrasonic waves in the coating is 0.076 m. What should be the time recorded if the coating is the correct thickness (1.00 mm)?

16.1 Traveling Waves Copyright © 2016 by OpenStax. All Rights Reserved.

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• Solar Eclipse 2024

See the 2024 Solar Eclipse’s Path of Totality

A total solar eclipse is expected to pass through the United States on April 8, 2024, giving stargazers across the country the opportunity to view the celestial phenomenon in which the sun is completely covered by the moon.

The eclipse will enter the U.S. in Texas and exit in Maine. It is the last time a total solar eclipse will be visible in the contiguous United States until 2044.

Here's what to know about the path of the eclipse and where you can see it.

Read More : How Animals and Nature React to an Eclipse

Where can you see the total solar eclipse?

The eclipse will cross through North America, passing over parts of Mexico, the United States, and Canada. 

The eclipse will enter the United States in Texas, and travel through Oklahoma, Arkansas, Missouri, Illinois, Kentucky, Indiana, Ohio, Pennsylvania, New York, Vermont, New Hampshire, and Maine. Small parts of Tennessee and Michigan will also experience the total solar eclipse.

Much of the eclipse's visibility depends on the weather. A cloudy day could prevent visitors from seeing the spectacle altogether.

When does the solar eclipse start and end?

The solar eclipse will begin in Mexico’s Pacific coast at around 11:07 a.m. PDT. It will exit continental North America on the Atlantic coast of Newfoundland, Canada, at 5:16 p.m. NDT.

The longest duration of totality—which is when the moon completely covers the sun — will be 4 minutes, 28 seconds, near Torreón, Mexico. Most places along the path of totality will see a totality duration between 3.5 and 4 minutes.

Read More : The Eclipse Could Bring $1.5 Billion Into States on the Path of Totality

Where’s the best place to see the total solar eclipse?

The best place to witness the event is along the path of totality. Thirteen states will be along the path of totality, and many towns across the country are preparing for the deluge of visitors— planning eclipse watch parties and events in the days leading up to totality.

In Rochester, NY, the Rochester Museum and Science Center is hosting a multi-day festival that includes a range of events and activities. Russellville, Arkansas will host an event with activities including live music, science presentations, tethered hot-air balloon rides, and telescope viewings.

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