surface waves travel through which medium

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 16.2 ).

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 wave s are governed by Newton’s laws and require a medium. A medium is the substance mechanical waves propagate 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, v = c = 2.99792458 × 10 8 m/s . v = c = 2.99792458 × 10 8 m/s . 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 .

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 .

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 16.3 . 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 16.3 , 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 f = 1 / T . f = 1 / T . 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 1 Hz = 1 s −1 . 1 Hz = 1 s −1 .

The length of the wave is called the wavelength and is represented by the Greek letter lambda ( λ ) ( λ ) , 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 16.3 , 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 + A + A above the equilibrium position, and the trough is a distance − A − A 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 v → . v → . 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 16.4 (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 16.4 (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 16.4 (b) is shown in Figure 16.5 . Figure 16.5 (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 16.5 (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.

Example 16.1

Wave on a string.

• 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 v = λ / T . v = λ / T .
• The first wave traveled 30.00 m in 6.00 s: v = 30.00 m 6.00 s = 5.00 m s . v = 30.00 m 6.00 s = 5.00 m s .
• The period is equal to the inverse of the frequency: T = 1 f = 1 2.00 s −1 = 0.50 s . T = 1 f = 1 2.00 s −1 = 0.50 s .
• The wavelength is equal to the velocity times the period: λ = v T = 5.00 m s ( 0.50 s ) = 2.50 m . λ = v T = 5.00 m s ( 0.50 s ) = 2.50 m .

Significance

Check your understanding 16.1.

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?

Example 16.2

Characteristics of a 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 v = λ T v = λ T and the frequency from f = 1 T . f = 1 T .
• The distance the wave traveled from time t = 0.00 s t = 0.00 s to time t = 3.00 s t = 3.00 s can be seen in the graph. Consider the red arrow, which shows the distance the crest has moved in 3 s. The distance is 8.00 cm − 2.00 cm = 6.00 cm . 8.00 cm − 2.00 cm = 6.00 cm . The velocity is v = Δ x Δ t = 8.00 cm − 2.00 cm 3.00 s − 0.00 s = 2.00 cm/s . v = Δ x Δ t = 8.00 cm − 2.00 cm 3.00 s − 0.00 s = 2.00 cm/s .
• The period is T = λ v = 8.00 cm 2.00 cm/s = 4.00 s T = λ v = 8.00 cm 2.00 cm/s = 4.00 s and the frequency is f = 1 T = 1 4.00 s = 0.25 Hz . f = 1 T = 1 4.00 s = 0.25 Hz .

Check Your Understanding 16.2

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?

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• Authors: William Moebs, Samuel J. Ling, Jeff Sanny
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• Book title: University Physics Volume 1
• Publication date: Sep 19, 2016
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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.

Mechanical Waves

Claimed by Snehil Mathur (Spring 2022)

Mechanical Waves are waves that propagate through a medium, one that is either solid, liquid, or gas. The speed at which a wave travels depends on the mediums' properties, both elastic and inertial.

• 1.1 A Mathematical Model
• 1.2 A Computational Model
• 2.2 Middling
• 2.3 Difficult
• 3 Connectedness
• 5.1 Further reading
• 5.2 External links
• 6 References

The Main Idea

Waves can be described as disturbances that travel through space and can transport energy from its source to another location. These are often represented in an oscillating manner.

Mechanical waves are waves that propagate through matter (gas, liquid, or solid) and require a medium in order to transport energy. Inherently, these waves cannot travel through a vacuum.

There are three main types of mechanical waves:

Transverse Waves:

Waves in which the particles oscillate back and forth in the direction perpendicular to the motion of the wave. The particle travels the length of the amplitude of the and completes its oscillation corresponding to when the wave moves over one wavelength. Some examples of transverse waves are ripples in the water and a vibrating string.

Longitudinal Waves:

Waves in which the particles move in the same direction as the wave motion. While still in an oscillating motion, they move "back-and-forth" with respect to the direction the wave is propagating in. Some examples of longitudinal waves include sound waves and the motion of compressing and stretching a spring.

Surface Waves:

Waves in which the particles within the medium move both parallel and perpendicular to the propagation direction of the wave. They're called surface waves due to their nature of travelling along the surface of a medium. This gives the particles on the wave a circular-like motion. The surface of a wave in the water is the most direct example of a surface wave; other examples include seismic waves and gravity waves along the surface of liquids.

A Mathematical Model

Mechanical waves implement a variety of equations that can be used to solve for different characteristics of a wave. The wave equation is used to find the speed of propagation of a transverse wave:

[math]\displaystyle{ v = \lambda f }[/math]

Where [math]\displaystyle{ v }[/math] is the velocity, [math]\displaystyle{ \lambda }[/math] is the wavelength, and [math]\displaystyle{ v }[/math] is the frequency. Another form of this equation specific to mechanical waves is the formula:

[math]\displaystyle{ v = \sqrt{Stiffness/Inertia} }[/math]

Another common form of this equation is the wave speed for a stretched string, [math]\displaystyle{ v = \sqrt{T/\mu} }[/math] , where [math]\displaystyle{ T }[/math] is the string tension and [math]\displaystyle{ \mu }[/math] is the mass per unit length of string. This equation allows for the calculation of the speed of a wave in different forms of matter. To find the equation of a wave that falls under two different mediums, we can apply superposition to find the new wave equation by adding the functions the two different functions that describe possible waves in the medium:

[math]\displaystyle{ y(x,t)=y_{1}+y_{2} }[/math]

Where [math]\displaystyle{ y_{1} }[/math] and [math]\displaystyle{ y_{2} }[/math] are the two possible wave functions for different mediums.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Q1) What kind of wave is a stadium wave?

A1) Transverse Wave

(The units of both of axis of this graph are in nm)

Find the speed of the wave described above:

A2) The wave equation to find the speed of this function is: [math]\displaystyle{ v = \lambda f }[/math] . To find the frequency, we apply the conversion from period to frequency: [math]\displaystyle{ f=1/T }[/math]

[math]\displaystyle{ f=\frac{1}{5*10^{-9}} = 2*10^8 }[/math]

To find the wavelength [math]\displaystyle{ \lambda }[/math] , we find the length it takes for the wave to complete on cycle. Based on the graph, we can visually verify that the wavelength is 10 nm. With both the wavelength and the frequency, we can calculate the speed:

[math]\displaystyle{ v = (2*10^9)(10*10^9) = \textbf{2*10^19} }[/math]

Q3) A transverse wave moves across a string. The wave can be represented with the equation [math]\displaystyle{ y(x,t)=0.5*sin(7x-3t) }[/math] with respect to it's position [math]\displaystyle{ x }[/math] in meters and time [math]\displaystyle{ t }[/math] in seconds. Find the amplitude, wavelength, period, and speed of the wave.

A3) For this question, we can use a lot of the wave functions we've learned from the past in order to convert the constants in this equation to the characteristics needed. First, we can write this equation as a form of its parent function:

[math]\displaystyle{ y(x,t)=Asin(kx-\omega t) }[/math]

Where [math]\displaystyle{ A }[/math] is the amplitude, [math]\displaystyle{ k }[/math] is the wave number, and [math]\displaystyle{ \omega }[/math] is the angular frequency. From reading the given equation, we can find:

[math]\displaystyle{ \textbf{Amplitude = 0.5 m} }[/math]

[math]\displaystyle{ k = 7 }[/math]

[math]\displaystyle{ \omega =3 }[/math]

We can use the wave number [math]\displaystyle{ k }[/math] to find the wavelength:

[math]\displaystyle{ k=\frac{2\pi}{\lambda} }[/math]

[math]\displaystyle{ \textbf{Wavelength = λ}=\frac{2\pi}{k}≈\textbf{0.898 m} }[/math]

To find the period [math]\displaystyle{ T }[/math] , we convert from the angular frequency with this equation:

[math]\displaystyle{ \omega =\frac{2\pi}{T} }[/math]

[math]\displaystyle{ \textbf{Period = T = }=\frac{2\pi}{\omega}≈\textbf{2.094 s} }[/math]

Finally, to find the speed, we can an altered version of the wave equation to substitute in [math]\displaystyle{ k }[/math] in order to make it easier:

[math]\displaystyle{ v=\frac{\omega}{k} }[/math]

[math]\displaystyle{ =\frac{3}{7}≈0.429 }[/math]

[math]\displaystyle{ \textbf{Speed = v ≈ 0.429} }[/math]

Connectedness

• This topic is connected to the way sound moves. They're created by an object vibrating and generating pulses of pressure waves that travel through the air and carry energy over distances.
• Wasn't able to find directly related information to mechanical waves

Connected topics include Electromagnetic Waves and Spring Motion.

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From Texas A&M University: [5]

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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) ).

Figure 16.2 From the world of renewable energy sources comes the electric power-generating buoy. Although there are many versions, this one converts the up-and-down motion, as well as side-to-side motion, of the buoy into rotational motion in order to turn an electric generator, which stores the energy in batteries.

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\,×\,{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.

Figure 16.3 An idealized surface water wave passes under a seagull that bobs up and down in simple harmonic motion. The wave has a wavelength [latex] \lambda [/latex], which is the distance between adjacent identical parts of the wave. The amplitude A of the wave is the maximum displacement of the wave from the equilibrium position, which is indicated by the dotted line. In this example, the medium moves up and down, whereas the disturbance of the surface propagates parallel to the surface at a speed v.

The water wave in the figure moves through the medium with a propagation velocity [latex] \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 .

Figure 16.4 (a) In a transverse wave, the medium oscillates perpendicular to the wave velocity. Here, the spring moves vertically up and down, while the wave propagates horizontally to the right. (b) In a longitudinal wave, the medium oscillates parallel to the propagation of the wave. In this case, the spring oscillates back and forth, while the wave propagates to the right.

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.

Figure 16.5 (a) This is a simple, graphical representation of a section of the stretched spring shown in (Figure)(b), representing the spring’s equilibrium position before any waves are induced on the spring. A point on the spring is marked by a blue dot. (b–g) Longitudinal waves are created by oscillating the end of the spring (not shown) back and forth along the x-axis. The longitudinal wave, with a wavelength [latex] \lambda [/latex], moves along the spring in the +x-direction with a wave speed v. For convenience, the wavelength is measured in (d). Note that the point on the spring that was marked with the blue dot moves back and forth a distance A from the equilibrium position, oscillating around the equilibrium position of the point.

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.

Figure 16.6 A transverse wave shown at two instants of time.

• 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]

Figure 16.7 Characteristics of the wave marked on a graph of its displacement.

• 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{\text{Δ}x}{\text{Δ}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⇒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 ⇒\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\,×\,{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] \text{Δ}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)?

• OpenStax University Physics. Authored by : OpenStax CNX. Located at : https://cnx.org/contents/[email protected]:Gofkr9Oy@15 . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

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• What is a Wave?

Waves come in many shapes and forms. While all waves share some basic characteristic properties and behaviors, some waves can be distinguished from others based on some observable (and some non-observable) characteristics. It is common to categorize waves based on these distinguishing characteristics.  

Longitudinal versus Transverse Waves versus Surface Waves

A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction that the wave moves. Suppose that a slinky is stretched out in a horizontal direction across the classroom and that a pulse is introduced into the slinky on the left end by vibrating the first coil up and down. Energy will begin to be transported through the slinky from left to right. As the energy is transported from left to right, the individual coils of the medium will be displaced upwards and downwards. In this case, the particles of the medium move perpendicular to the direction that the pulse moves. This type of wave is a transverse wave. Transverse waves are always characterized by particle motion being perpendicular to wave motion.

A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves. Suppose that a slinky is stretched out in a horizontal direction across the classroom and that a pulse is introduced into the slinky on the left end by vibrating the first coil left and right. Energy will begin to be transported through the slinky from left to right. As the energy is transported from left to right, the individual coils of the medium will be displaced leftwards and rightwards. In this case, the particles of the medium move parallel to the direction that the pulse moves. This type of wave is a longitudinal wave. Longitudinal waves are always characterized by particle motion being parallel to wave motion.

A sound wave traveling through air is a classic example of a longitudinal wave. As a sound wave moves from the lips of a speaker to the ear of a listener, particles of air vibrate back and forth in the same direction and the opposite direction of energy transport. Each individual particle pushes on its neighboring particle so as to push it forward. The collision of particle #1 with its neighbor serves to restore particle #1 to its original position and displace particle #2 in a forward direction. This back and forth motion of particles in the direction of energy transport creates regions within the medium where the particles are pressed together and other regions where the particles are spread apart. Longitudinal waves can always be quickly identified by the presence of such regions. This process continues along the chain of particles until the sound wave reaches the ear of the listener. A detailed discussion of sound is presented in another unit of The Physics Classroom Tutorial .

Waves traveling through a solid medium can be either transverse waves or longitudinal waves. Yet waves traveling through the bulk of a fluid (such as a liquid or a gas) are always longitudinal waves. Transverse waves require a relatively rigid medium in order to transmit their energy. As one particle begins to move it must be able to exert a pull on its nearest neighbor. If the medium is not rigid as is the case with fluids, the particles will slide past each other. This sliding action that is characteristic of liquids and gases prevents one particle from displacing its neighbor in a direction perpendicular to the energy transport. It is for this reason that only longitudinal waves are observed moving through the bulk of liquids such as our oceans. Earthquakes are capable of producing both transverse and longitudinal waves that travel through the solid structures of the Earth. When seismologists began to study earthquake waves they noticed that only longitudinal waves were capable of traveling through the core of the Earth. For this reason, geologists believe that the Earth's core consists of a liquid - most likely molten iron.

While waves that travel within the depths of the ocean are longitudinal waves, the waves that travel along the surface of the oceans are referred to as surface waves. A surface wave is a wave in which particles of the medium undergo a circular motion. Surface waves are neither longitudinal nor transverse. In longitudinal and transverse waves, all the particles in the entire bulk of the medium move in a parallel and a perpendicular direction (respectively) relative to the direction of energy transport. In a surface wave, it is only the particles at the surface of the medium that undergo the circular motion. The motion of particles tends to decrease as one proceeds further from the surface.

Any wave moving through a medium has a source. Somewhere along the medium, there was an initial displacement of one of the particles. For a slinky wave, it is usually the first coil that becomes displaced by the hand of a person. For a sound wave, it is usually the vibration of the vocal chords or a guitar string that sets the first particle of air in vibrational motion. At the location where the wave is introduced into the medium, the particles that are displaced from their equilibrium position always moves in the same direction as the source of the vibration. So if you wish to create a transverse wave in a slinky, then the first coil of the slinky must be displaced in a direction perpendicular to the entire slinky. Similarly, if you wish to create a longitudinal wave in a slinky, then the first coil of the slinky must be displaced in a direction parallel to the entire slinky.

Electromagnetic versus Mechanical Waves

Another way to categorize waves is on the basis of their ability or inability to transmit energy through a vacuum (i.e., empty space). Categorizing waves on this basis leads to two notable categories: electromagnetic waves and mechanical waves.

An electromagnetic wave is a wave that is capable of transmitting its energy through a vacuum (i.e., empty space). Electromagnetic waves are produced by the vibration of charged particles. Electromagnetic waves that are produced on the sun subsequently travel to Earth through the vacuum of outer space. Were it not for the ability of electromagnetic waves to travel to through a vacuum, there would undoubtedly be no life on Earth. All light waves are examples of electromagnetic waves. Light waves are the topic of another unit at The Physics Classroom Tutorial . While the basic properties and behaviors of light will be discussed, the detailed nature of an electromagnetic wave is quite complicated and beyond the scope of The Physics Classroom Tutorial .

A mechanical wave is a wave that is not capable of transmitting its energy through a vacuum. Mechanical waves require a medium in order to transport their energy from one location to another. A sound wave is an example of a mechanical wave. Sound waves are incapable of traveling through a vacuum. Slinky waves, water waves, stadium waves, and jump rope waves are other examples of mechanical waves; each requires some medium in order to exist. A slinky wave requires the coils of the slinky; a water wave requires water; a stadium wave requires fans in a stadium; and a jump rope wave requires a jump rope.

The above categories represent just a few of the ways in which physicists categorize waves in order to compare and contrast their behaviors and characteristic properties. This listing of categories is not exhaustive; there are other categories as well. The five categories of waves listed here will be used periodically throughout this unit on waves as well as the units on sound and light .

Investigate!

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Check Your Understanding

1. A transverse wave is transporting energy from east to west. The particles of the medium will move_____.

a. east to west only b. both eastward and westward c. north to south only d. both northward and southward

The particles would be moving back and forth in a direction perpendicular to energy transport. The waves are moving westward, so the particles move northward and southward.

2.A wave is transporting energy from left to right. The particles of the medium are moving back and forth in a leftward and rightward direction. This type of wave is known as a ____.

a. mechanical b. electromagnetic c. transverse d. longitudinal

The particles are moving parallel to the direction that the wave is moving. This must be a longitudinal wave.

3. Describe how the fans in a stadium must move in order to produce a longitudinal stadium wave.

The fans will need to sway side to side. Thus, as the wave travels around the stadium they would be moving parallel to its direction of motion. If they rise up and sit down, then they would be creating a transverse wave.

4. A sound wave is a mechanical wave, not an electromagnetic wave. This means that

a. particles of the medium move perpendicular to the direction of energy transport. b. a sound wave transports its energy through a vacuum. c. particles of the medium regularly and repeatedly oscillate about their rest position. d. a medium is required in order for sound waves to transport energy.

Mechanical waves require a medium in order to transport energy. Sound, like any mechanical wave, cannot travel through a vacuum.

5. A science fiction film depicts inhabitants of one spaceship (in outer space) hearing the sound of a nearby spaceship as it zooms past at high speeds. Critique the physics of this film.

This is an example of faulty physics in film. Sound is a mechanical wave and could never be transmitted through the vacuum of outer space.

6. If you strike a horizontal rod vertically from above, what can be said about the waves created in the rod?

a. The particles vibrate horizontally along the direction of the rod. b. The particles vibrate vertically, perpendicular to the direction of the rod. c. The particles vibrate in circles, perpendicular to the direction of the rod. d. The particles travel along the rod from the point of impact to its end.

The particles vibrate in the direction of the source which creates the initial disturbance. Since the hammer was moving vertically, the particles will also vibrate vertically.

7. Which of the following is not a characteristic of mechanical waves?

a. They consist of disturbances or oscillations of a medium. b. They transport energy. c. They travel in a direction that is at right angles to the direction of the particles of the medium. d. They are created by a vibrating source.

The characteristic described in statement c is a property of all transverse waves, but not necessarily of all mechanical waves. A mechanical wave can also be longitudinal.

8. The sonar device on a fishing boat uses underwater sound to locate fish. Would you expect sonar to be a longitudinal or a transverse wave?

Answer: Longitudinal

Only longitudinal waves are capable of traveling through fluids such as water. When a transverse wave tries to propagate through water, the particles of the medium slip past each other and so prevent the movement of the wave.

• Anatomy of a Wave

When an earthquake occurs, it releases energy waves, known as Seismic waves. It is like the ripples created in water if you throw a stone in it. Seismic waves are like ripples that can travel through the inside of the earth and on the surface.

Types of Earthquake Waves

Based on the medium they travel in, earthquake waves can be classified under two categories:

• Surface waves

Body waves are those waves that travel through the earth. They originate at the epicentre of the earthquake and travel through the earth at amazing speeds. There are two types of body waves, namely,

Surface waves are those waves that travel on the surface of the earth. The destruction caused by earthquakes is primarily done by these waves.

S waves and P waves

S waves  also called secondary waves and shear waves, are the second waves to hit the seismographs. They are transverse waves, which means that the motion is perpendicular to the direction of wave propagation . S waves can only travel through solids, and scientists have successfully mapped the earth’s interior by studying the routes of these waves.

P waves  or Primary waves are the first waves to hit the seismographs when an earthquake strikes. They are longitudinal waves which means that the direction of motion and propagation are the same.

Difference between p waves and s waves

Frequently asked questions – faqs, what is an earthquake, what are seismic waves, what are the two types of seismic waves, what are the two types of body waves, what are p waves, watch the video and discover what an earthquake is and what causes it..

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why surface wave is important for geographical studies?

Seismic waves are important in geology and not geography. Geography explains how human culture impacts the natural environment and how different regions influence the people living there. Geology discusses the Earth’s structure, composition, and changes over time.

Geologists investigate the deep layers of the Earth’s crust by examining how seismic waves traverse through the Earth.

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Lesson 6: Seismic Waves

In this lesson, students learn about different types of seismic waves on the basis of where and how the waves move. In addition, students discuss how scientists use earthquake waves to investigate the interior structure of the Earth.

This activity is designed for one 1-hour class period.

• A few slinkies
• 1' of white (or other brightly-colored) plastic tape
• One 2-meter rope

Introduction

2. Encourage students to discuss how they think the elastic energy travels to the surface of the Earth or whether they think it passes through the entire Earth. Use a simple example: Ask students to predict what would happen if they touch one end of a brick and tap the other end with a hammer. If you have a brick and a hammer, allow students to experiment with them. Students should be able to feel the energy of the hammer in their fingertips. Encourage students to guess why they can feel the energy. Explain to them that they can feel it because the energy of the hammer blows travels to their fingertips in the form of waves.

3. Explain to students that earthquake energy travels in the form of waves. These waves are called seismic or earthquake waves. There are different kinds of earthquake waves: body waves and surface waves. Body waves pass through the interior of the Earth whereas surface waves travel along the Earth's surface. Explain that earthquake waves move particles of material in different ways: whereas, compressional waves create a back and forth motion parallel to the direction of the waves, shear waves create a back and forth motion perpendicular to the direction of the waves.

4. Ask your students where they think the seismic waves of an earthquake originate. Students may answer: along the fault plane or at a single point along the fault. Introduce to your students these two terms: hypocenter (focus) and epicenter. While the focus of an earthquake is where rock ruptures and slips, the epicenter is the point on the surface of the Earth that lies directly above the focus.

Caution: While the first seismic waves radiate from the focus, later waves may originate from anywhere across the area of slip. Therefore, all the energy of an earthquake is not always radiated from the focus, and for this reason the focus of an earthquake is not always the only source of seismic waves (Wampler, 2002).

5. Encourage students to think about other kinds of energy that travel in the form of waves (e.g. sound, light). Explain to students when a train whistle screams, the sound they hear has moved through the air from the whistle to their ears in the form of sound waves. Explain to them that waves are disturbances that transmit energy from one point to another by causing periodic (back and forth) motions. The whistle causes the nearby air molecules to vibrate. As molecules begin to vibrate, they bump against each other and cause the neighboring molecules to vibrate. When the molecules next to their ears start to vibrate, that is when they hear the whistle. Ask students if they can hear sounds in outer space where there is no air. The answer is no. Sound energy cannot travel through a vacuum because there is no medium to be disturbed or vibrated. Ask students if sound energy can travel through solids or liquids. The answer is yes. Sound energy can cause molecules in solids or liquids to vibrate. Ask students why sound energy can travel through solids faster than liquids. Explain to students that in solids, molecules are closer to each other, and can therefore bump each other more quickly.

Note: Some people may hear earthquakes when earthquake waves travel through the ground (from a rumble to a boom). This is because earthquakes can sometimes generate sound waves in the audible frequency range. The sound energy travels through the ground, but it can also be transmitted into the air.

2. Direct students in each group/pair to mark two spots on their slinky near the center with plastic tape at the top of adjacent loops. Students mark the coils so that they can see the movement of energy along their length.

3. Have two students each hold one end of the slinky for their group. Stretch out the slinky to about 3 meters along a floor, table, or other flat surface. Have students take turns compressing 10–20 coils and then releasing them rapidly while they hold the end of the slinky, making sure to watch the energy wave travel the length of the slinky.

4. After several repetitions, ask students to describe their observations of the coil and the tape: the coils move back and forth along the length of the slinky as they compress and expand it. Ask students what kind of earthquake waves this slinky motion resembles. The answer is compressional waves. Remind them that in compressional waves particles of material move back and forth parallel to the direction in which the wave itself moves. As a compressional wave passes, the material first compresses and then expands. P-waves (P stands for primary) are compressional earthquake waves that pass through the interior of the Earth. P-waves change the volume of the material through which they propagate.

Note: P-waves in the air are sounds. P-waves can move faster through the ground than the air, but not all of this energy is in the range of human hearing. When the sound waves are in the audible frequency range, some people may hear them.

5. Now tie one end of a 2-meter rope to the door knob of the classroom door. Ask one student to hold the free end of the rope in his/her hand. Ask the student to back away from the door until the rope is straight with a little bit of slack and start to gently shake the rope up and down. Allow each student to create this motion. After several repetitions, ask students to describe the rope motion. Ask them what kind of earthquake wave motion this resembles. The answer is shear waves. Remind them that in shear waves particles of material move back and forth perpendicular to the direction in which the wave itself moves. S-waves (S stands for secondary) are shear earthquake waves that pass through the interior of the Earth. S-waves don't change the volume of the material through which they propagate, they shear it.

Note: The motion of the rope due to shear waves is much easier to observe than the compression waves, but the shear waves travel more slowly than compression waves. In an earthquake, scientists can observe the arrival of compression waves before the arrival of shear waves using seismographs. You may choose to show a close-up of a record (seismogram) for a single earthquake event, and ask your students to point out different seismic waves. In addition, shear waves cause much more damage to structures since it is easier to shake surface rocks than it is to compress them.

6. Encourage your students to critically evaluate their slinky and rope setup. Ask them if they see any limitations associated with their setup. Ask them to compare and contrast their simple setup with actual vibrations caused by seismic waves traveling through the Earth or along its surface. For instance, seismic waves carry energy from the source of the shaking outward in all directions (not in one direction only as the setup shows).

7. (Optional) Both primary and secondary waves are body waves (pass through the interior of the Earth). Surface waves travel along the Earth's surface. Two examples of surface waves are Rayleigh waves and Love waves. Explain to your students that Rayleigh waves cause the ground to ripple up and down (like water waves in the ocean before they break at the surf line) whereas the Love waves cause the ground to ripple back and forth (like the movement of a snake).

8. Ask the students to recall how scientists use seismic wave observations to investigate the interior structure of the Earth. This is similar to checking the ripeness of a melon by tapping on it. To understand how scientists see into the Earth using vibrations, one needs to understand how waves or vibrations interact with the rocks that make up the Earth. Introduce to your students the two simplest types of wave interactions with rocks: reflection and refraction. Ask students to define reflection. They should be able to give simple examples like echoes or reflection in a mirror. Explain to your students that echoes are reflected sound waves, and that students' reflections in a mirror are composed of reflected light waves. Tell students that a seismic reflection happens when a wave impinges on a change in rock type. Part of the energy carried by the wave is transmitted through the material (refracted wave) and part is reflected back into the medium that contained the wave. Refraction can be demonstrated by dropping a coin in a bottle filled with water. The coin changes direction when it hits the water's surface and won't sink to the bottom vertically. In other words, the path of the coin refracts (changes direction) when moving from the air into the water.

9. Explain to students that seismic waves travel fast, on the order of kilometers per second. The speed of a seismic wave depends on many factors. Ask students to think about a few factors that can change the speed of a seismic wave (e.g., rock composition, temperature, pressure) Ask them to explain how these factors can change the speed of a seismic wave. Students should be able to answer these questions based on the knowledge they acquired throughout this lesson. Seismic waves travel faster in denser rocks; temperature tends to lower the speed of seismic waves; and pressure tends to increases the speed.

Caution: The speed of a seismic wave generally increases with depth, despite the fact that the increase of temperature with depth works to lower the wave velocity.

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