Transverse Waves

A transverse wave is a wave in which the particles of the medium move perpendicular (at right angles) to the direction in which the wave travels.

For example, imagine a rope stretched horizontally. If one end of the rope is moved up and down, a wave travels along the rope horizontally while sections of the rope move vertically.

So there are two different directions:

• Wave direction: forward along the rope
• Particle motion: up and down
• These directions are perpendicular to each other.

This perpendicular motion is the defining feature of a transverse wave.

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Waves Transfer Energy

A wave is a disturbance that transfers energy from one place to another.

When a transverse wave travels through a rope, the wave moves along the rope, but the individual pieces of rope do not travel with the wave.

Instead, each section moves up and down around its normal position.

For example, if a pulse travels 5 m along a rope, a small piece of the rope does not move 5 m horizontally. It mainly moves up and down as the disturbance passes.

This illustrates an important principle:

Waves transfer energy without transferring matter from one location to another overall.

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Particle Motion in a Transverse Wave

The word transverse means across or sideways.

In a transverse wave, particle motion is across the direction of wave travel.

If the wave travels:

→

the particles might move:

↑ ↓

The motions are at right angles:

particle motion ⟂ wave direction

The symbol ⟂ means perpendicular to.

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A Wave on a Rope

A rope provides one of the easiest ways to observe a transverse wave.

Imagine holding one end of a long rope while another person holds the opposite end.

Move your hand upward and then downward.

The disturbance travels along the rope.

Your hand moves:

up and down

The wave travels:

along the rope

These directions are perpendicular.

The rope itself does not travel from one person to the other. Instead, the disturbance and its energy travel along the rope.

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Equilibrium Position

Before a wave passes, the particles of a medium have a normal resting position.

This is called the equilibrium position.

For a horizontal rope, the equilibrium position can be imagined as a straight horizontal line.

As a transverse wave passes, particles move:

• above equilibrium
• back through equilibrium
• below equilibrium
• back toward equilibrium

They oscillate around this central position.

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Oscillation

An oscillation is repeated movement back and forth around an equilibrium position.

In a transverse wave, particles oscillate perpendicular to the direction of wave travel.

For example, a point on a rope may repeatedly move:

up → equilibrium → down → equilibrium → up

while the wave continues travelling horizontally.

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The Shape of a Transverse Wave

A transverse wave is often represented with a familiar wave shape containing peaks and valleys.

Important features include:

• equilibrium position
• crest
• trough
• amplitude
• wavelength

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Crest

The crest is the highest point of a transverse wave above its equilibrium position.

It represents the maximum displacement in one direction.

If the equilibrium position is considered zero displacement, a crest has maximum positive displacement.

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Trough

The trough is the lowest point of a transverse wave below its equilibrium position.

It represents maximum displacement in the opposite direction.

Crests and troughs are characteristic features used when describing transverse wave diagrams.

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Amplitude

The amplitude of a wave is the maximum displacement from the equilibrium position.

Amplitude is measured from:

equilibrium → crest

or:

equilibrium → trough

It is not normally measured from crest to trough.

If the distance from a crest to the equilibrium position is 4 cm:

amplitude = 4 cm

If the total vertical distance from crest to trough is 8 cm:

amplitude = 8/2 = 4 cm

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Amplitude and Energy

A larger amplitude generally represents a wave carrying more energy.

For example, shaking a rope gently produces a small-amplitude wave.

Moving the rope much more strongly can produce a larger-amplitude wave.

The exact relationship between amplitude and energy depends on the type of wave, but a useful general rule is:

greater amplitude → greater energy

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Wavelength

Wavelength is the distance between two corresponding points on consecutive waves.

The symbol for wavelength is:

λ

The Greek letter λ is pronounced lambda.

Wavelength can be measured from:

• crest to next crest
• trough to next trough
• any point to the next identical point in the wave cycle

Wavelength is a distance, so its SI unit is:

metre (m)

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Measuring Wavelength Correctly

Suppose the distance from one crest to the next crest is:

2.5 m

Then:

λ = 2.5 m

The distance from a crest to the neighbouring trough is not one full wavelength.

For a regular wave:

crest to neighbouring trough = λ/2

So if crest-to-trough horizontal distance is 1.25 m:

λ = 2(1.25)

λ = 2.5 m

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Frequency

Frequency is the number of complete wave cycles passing a point each second.

Its symbol is:

f

Its unit is:

hertz (Hz)

For example:

f = 5 Hz

means:

5 complete cycles occur each second.

Although frequency is not unique to transverse waves, it is an important property used to describe them.

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Period

The period is the time required for one complete wave cycle.

Its symbol is:

T

Its unit is:

second (s)

Frequency and period are related:

f = 1/T

and:

T = 1/f

If:

f = 4 Hz

then:

T = 1/4

T = 0.25 s

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Wave Speed

Wave speed describes how quickly a wave travels.

The basic relationship is:

v = fλ

where:

v = wave speed in m/s

f = frequency in Hz

λ = wavelength in m

For example, if:

f = 5 Hz

λ = 2 m

then:

v = 5 × 2

v = 10 m/s

The particles of the medium do not necessarily move forward at this speed. This equation describes the speed of the wave disturbance.

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Example of a Transverse Wave Calculation

A transverse wave has:

frequency = 8 Hz

wavelength = 0.50 m

Find the wave speed.

Use:

v = fλ

Substitute:

v = 8 × 0.50

v = 4.0 m/s

The wave travels at 4.0 m/s.

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Examples of Transverse Waves

Examples commonly associated with transverse waves include:

• waves on stretched ropes
• waves on strings
• electromagnetic waves
• light
• radio waves
• microwaves
• infrared radiation
• ultraviolet radiation
• X-rays
• gamma rays

Surface water waves are also often used to illustrate transverse-like motion, although real water-wave particle motion is more complicated than a simple transverse wave.

---

Waves on Strings

Strings can support transverse waves.

Examples include:

• guitar strings
• violin strings
• piano strings
• stretched cords
• laboratory wave strings

When a guitar string vibrates, sections of the string move back and forth perpendicular to the length of the string.

The vibration can produce sound by causing the surrounding air and the guitar body to vibrate.

---

Electromagnetic Waves

Electromagnetic waves are transverse waves.

Examples include:

• radio waves
• microwaves
• infrared
• visible light
• ultraviolet
• X-rays
• gamma rays

Unlike mechanical waves on a rope, electromagnetic waves do not require a material medium.

This means light can travel through the vacuum of space.

That is why energy from the Sun can reach Earth.

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What Oscillates in an Electromagnetic Wave?

In electromagnetic waves, there are no material particles that must move up and down.

Instead, electric and magnetic fields oscillate.

These fields oscillate perpendicular to the direction of wave travel.

Therefore, electromagnetic waves are classified as transverse.

This is an important distinction:

Mechanical transverse wave: particles of a medium oscillate.

Electromagnetic transverse wave: electric and magnetic fields oscillate.

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Water Waves

Water waves are often shown as examples of transverse waves because the water surface moves up and down while the wave travels horizontally.

However, real water waves are more complicated.

Water particles near the surface can move in approximately circular or elliptical paths rather than simply moving vertically.

Therefore, surface water waves have characteristics of both transverse and longitudinal motion.

For introductory wave diagrams, however, they are useful for visualizing crests, troughs, amplitude, and wavelength.

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Longitudinal Waves

A longitudinal wave is different from a transverse wave.

In a longitudinal wave, particles move parallel to the direction in which the wave travels.

If the wave travels:

→

the particles also oscillate:

↔

Examples include:

• sound waves in air
• compression waves in springs
• some seismic waves

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Transverse vs Longitudinal Waves

The main difference is the relationship between particle motion and wave direction.

The most important comparison is:

Transverse: particle motion ⟂ wave direction

Longitudinal: particle motion ∥ wave direction

The symbol ∥ means parallel to.

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Compressions and Rarefactions

Longitudinal waves do not have crests and troughs in the same physical sense as transverse displacement waves.

Instead, they contain:

Compressions — regions where particles are closer together.

Rarefactions — regions where particles are farther apart.

This can be demonstrated using a spring or slinky.

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Comparing Rope Waves and Sound Waves

Consider a transverse wave travelling along a rope.

The wave moves horizontally while the rope moves vertically.

Now consider a sound wave travelling through air.

The sound travels forward while air particles vibrate backward and forward in approximately the same direction as the wave.

Therefore:

rope wave → transverse

sound wave in air → longitudinal

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Direction Is the Key

Do not classify a wave as transverse simply because its diagram looks like a wavy line.

Instead, ask:

In what direction does the wave travel?

Then ask:

In what direction does the disturbance oscillate?

If these directions are perpendicular:

transverse

If these directions are parallel:

longitudinal

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Representing a Transverse Wave

A simple transverse wave sketch should show a repeating pattern above and below an equilibrium line.

Important features to identify include:

• equilibrium position
• crests
• troughs
• amplitude
• wavelength
• direction of wave travel
• direction of particle motion

The directions of particle motion and wave travel should be perpendicular.

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How to Sketch a Transverse Wave

To create a useful sketch:

1. Draw a horizontal equilibrium line.
2. Draw a smooth repeating wave above and below the line.
3. Identify at least two crests.
4. Identify at least two troughs.
5. Show amplitude from equilibrium to a crest or trough.
6. Show wavelength from one crest to the next crest.
7. Show the direction in which the wave travels.
8. Show particle motion perpendicular to the wave direction.

The sketch should communicate the physics, not merely look like a curved line.

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Reading a Transverse Wave Diagram

Suppose a wave diagram shows:

crest-to-crest distance = 6 m

equilibrium-to-crest distance = 2 m

Then:

wavelength = 6 m

amplitude = 2 m

If the crest-to-trough vertical distance is shown as 4 m, this confirms:

amplitude = 4/2

amplitude = 2 m

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Counting Wavelengths

Suppose the distance from the first crest to the fourth crest is:

12 m

From the first crest to the fourth crest there are:

3 complete wavelengths

Therefore:

3λ = 12

λ = 12/3

λ = 4 m

A common mistake is to count crests rather than the spaces between corresponding crests.

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Particle Motion at a Point

Imagine placing a small marker on a rope.

As a transverse wave passes, the marker may move:

• upward
• downward
• upward again

But it remains approximately in the same horizontal region.

Watching the marker makes it easier to distinguish:

movement of the medium

from:

movement of the wave

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Wave Motion Is Not Particle Transport

Suppose a wave travels from one end of a 10 m rope to the other.

It does not mean that the particles at one end travel 10 m along the rope.

Instead, neighbouring particles interact and transfer the disturbance.

This is similar to spectators performing a stadium wave.

Each person moves mainly up and down, but the wave pattern travels around the stadium.

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Energy and Matter

The stadium-wave analogy demonstrates an important idea.

The people do not run around the stadium with the wave.

Instead:

people oscillate locally

while:

the wave pattern travels

Likewise, waves can transfer energy through a medium without carrying the medium itself from the source to the destination.

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Transverse Waves in Technology

Transverse waves are important in many technologies.

Electromagnetic transverse waves are used in:

• radio communication
• mobile communication
• Wi-Fi
• satellite communication
• medical imaging
• remote controls
• fibre-optic communication

Understanding transverse waves helps explain how information and energy can travel over large distances.

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Seismic Waves

Earthquakes produce several types of seismic waves.

S-waves are transverse seismic waves.

In an S-wave, material moves perpendicular to the direction in which the seismic wave travels.

S-waves cannot travel through liquids, which helped scientists develop evidence about Earth's internal structure.

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Transverse Waves and Polarization

A special property of transverse waves is that they can be polarized.

Polarization restricts oscillations to a particular direction.

For example, light normally contains electromagnetic oscillations in different orientations. A polarizing filter allows particular orientations to pass.

This provides important evidence that light is transverse.

Applications include:

• polarized sunglasses
• photography filters
• LCD technology
• scientific instruments

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A Complete Example

A transverse wave travels along a rope.

The distance between consecutive crests is:

1.5 m

The maximum displacement from equilibrium is:

0.25 m

The frequency is:

4 Hz

Therefore:

wavelength:

λ = 1.5 m

amplitude:

A = 0.25 m

wave speed:

v = fλ

v = 4 × 1.5

v = 6 m/s

If the wave travels horizontally, particles of the rope oscillate vertically.

This example combines the major features used to describe a transverse wave.

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Identifying a Transverse Wave

When deciding whether a wave is transverse, use this process:

1. Identify the direction of wave travel.
2. Identify the direction of the oscillation.
3. Compare the two directions.
4. If they are perpendicular, classify the wave as transverse.
5. Identify crests and troughs where appropriate.
6. Identify amplitude and wavelength if shown.
7. Remember that the wave transfers energy while particles oscillate locally.

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Common Mistakes

Thinking particles travel with the wave

Particles usually oscillate around equilibrium while the wave disturbance travels.

Thinking every wavy-looking diagram represents a transverse wave

Classification depends on the direction of oscillation relative to wave travel.

Confusing amplitude and wavelength

Amplitude measures displacement from equilibrium.

Wavelength measures the distance between corresponding points on consecutive waves.

Measuring amplitude from crest to trough

Crest-to-trough height is twice the amplitude.

Measuring wavelength from crest to neighbouring trough

This represents half a wavelength for a regular sinusoidal wave.

Saying transverse particles move parallel to the wave

They move perpendicular to the wave direction.

Calling the lowest point a compression

The lowest point of a transverse wave is a trough. Compressions belong to longitudinal waves.

Assuming all transverse waves require matter

Electromagnetic waves are transverse and can travel through a vacuum.

Assuming water particles simply move vertically

Real surface-water particle motion is more complex and often approximately circular or elliptical.

Counting crests instead of wavelengths

Count complete intervals between corresponding points.

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Key Terms

Wave — disturbance that transfers energy from one location to another.

Transverse wave — wave in which oscillation occurs perpendicular to the direction of wave travel.

Longitudinal wave — wave in which particle oscillation occurs parallel to the direction of wave travel.

Medium — material through which a mechanical wave travels.

Oscillation — repeated motion around an equilibrium position.

Equilibrium position — normal resting position of particles in a medium.

Crest — highest point of a transverse wave relative to equilibrium.

Trough — lowest point of a transverse wave relative to equilibrium.

Amplitude — maximum displacement from equilibrium.

Wavelength (λ) — distance between corresponding points on consecutive waves.

Frequency (f) — number of complete cycles occurring each second, measured in hertz.

Period (T) — time required for one complete cycle.

Wave speed (v) — speed at which the wave disturbance travels.

Compression — region of a longitudinal wave where particles are closer together.

Rarefaction — region of a longitudinal wave where particles are farther apart.

Electromagnetic wave — transverse oscillation of electric and magnetic fields that can travel through a vacuum.

S-wave — transverse seismic wave produced by earthquakes.

Polarization — restriction of transverse oscillations to particular orientations.

Particle motion — movement of particles of a medium as a mechanical wave passes.

Wave direction — direction in which the disturbance and its energy propagate.

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Key Takeaways

• A transverse wave has oscillations perpendicular to the direction of wave travel.
• A wave transfers energy without transporting matter overall from source to destination.
• Particles in a mechanical transverse wave oscillate around an equilibrium position.
• A rope wave is a useful model for visualizing transverse motion.
• Crests are maximum displacements above equilibrium.
• Troughs are maximum displacements below equilibrium.
• Amplitude is measured from equilibrium to a crest or trough.
• Wavelength is the distance between consecutive corresponding points.
• Frequency measures the number of cycles per second.
• Period measures the time for one complete cycle.
• Wave speed can be calculated using v = fλ.
• Mechanical transverse waves require a medium.
• Electromagnetic waves are transverse but do not require a material medium.
• Light, radio waves, microwaves, X-rays, and other electromagnetic waves are transverse.
• Surface water waves are more complicated than purely transverse waves.
• Longitudinal waves have particle motion parallel to wave travel.
• Longitudinal waves contain compressions and rarefactions rather than physical crests and troughs.
• S-waves are transverse seismic waves.
• Polarization is a characteristic property of transverse waves.
• A correct transverse-wave sketch should show the equilibrium position, crests, troughs, amplitude, wavelength, wave direction, and particle-motion direction.
• The most reliable way to identify a transverse wave is to compare the direction of oscillation with the direction of wave travel.

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Check Your Understanding

1. Define a transverse wave in terms of the direction of particle motion and wave travel.
2. A wave travels horizontally to the right while particles move vertically up and down. Is the wave transverse or longitudinal? Explain.
3. Explain the difference between the motion of a wave along a rope and the motion of an individual section of the rope.
4. Define crest, trough, and equilibrium position.
5. A wave has a vertical crest-to-trough distance of 12 cm. Determine its amplitude.
6. The distance between consecutive crests is 3.5 m. Determine the wavelength.
7. The distance from the first crest to the fifth crest is 16 m. Determine the wavelength.
8. A transverse wave has a wavelength of 2.0 m and frequency of 6 Hz. Calculate its wave speed.
9. A wave travels at 24 m/s and has a wavelength of 3 m. Calculate its frequency.
10. Compare transverse and longitudinal waves in terms of particle motion and wave direction.
11. Explain why sound travelling through air is classified as longitudinal rather than transverse.
12. Explain why light can be classified as transverse even though there are no material particles oscillating as light travels through a vacuum.
13. Sketch a transverse wave containing at least two complete wavelengths. Identify the equilibrium position, a crest, a trough, amplitude, wavelength, wave direction, and particle-motion direction.
14. A student says, "The wave travelled 5 m along the rope, so each particle of the rope must also have travelled 5 m." Explain the student's mistake.
15. A wave diagram shows repeated peaks and valleys. Explain why the shape of the diagram alone is not enough to prove that the wave is transverse and describe the evidence needed to classify the wave correctly.

Longitudinal Waves

A longitudinal wave is a wave in which the particles of a medium vibrate parallel to the direction in which the wave travels.

Imagine pushing and pulling one end of a stretched spring or slinky. Sections of the spring move backward and forward while the disturbance travels along the length of the spring.

If the wave travels:

→

the particles oscillate:

↔

The particle motion and wave direction are therefore parallel.

This parallel motion is the defining feature of a longitudinal wave.

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Waves Transfer Energy

Like all waves, longitudinal waves transfer energy from one location to another.

However, the particles of the medium do not travel along with the wave over large distances.

Instead, they oscillate backward and forward around their equilibrium positions.

For example, when sound travels across a classroom, air molecules do not travel all the way from the speaker to the listener.

Instead:

• one group of air molecules vibrates
• these molecules interact with neighbouring molecules
• the disturbance passes through the air
• energy travels across the room

The matter itself mainly oscillates locally.

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Particle Motion in a Longitudinal Wave

The most important feature of a longitudinal wave is the relationship between:

• particle motion
• wave direction

Suppose a longitudinal wave travels to the right.

The particles move:

backward and forward

along the same line.

Therefore:

particle motion ∥ wave direction

The symbol ∥ means parallel to.

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A Longitudinal Wave in a Spring

A spring or slinky provides an excellent model of a longitudinal wave.

If several coils are pushed together and released, the compressed region travels along the spring.

The individual coils do not travel from one end of the spring to the other.

Instead, each coil moves backward and forward around its normal position.

The travelling pattern consists of alternating:

• compressions
• rarefactions

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Compressions

A compression is a region of a longitudinal wave where particles are closer together than normal.

In a spring:

compression = coils close together

In a sound wave:

compression = air molecules temporarily crowded together

A compression generally corresponds to:

• higher particle density
• higher pressure

than the surrounding undisturbed medium.

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Rarefactions

A rarefaction is a region where particles are farther apart than normal.

In a spring:

rarefaction = coils spread farther apart

In air:

rarefaction = air molecules temporarily farther apart

A rarefaction generally corresponds to:

• lower particle density
• lower pressure

than the surrounding undisturbed medium.

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Alternating Compressions and Rarefactions

A longitudinal wave consists of a repeating pattern:

compression → rarefaction → compression → rarefaction

As this pattern travels through the medium, individual particles oscillate backward and forward.

The particles themselves do not permanently remain compressed or spread apart.

Instead, different regions become compressed and rarefied as the disturbance passes.

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Equilibrium Position

Particles in a medium normally have an equilibrium position.

When a longitudinal wave passes, particles are temporarily displaced from equilibrium.

They then move back toward equilibrium and may continue past it.

This produces an oscillation:

forward → equilibrium → backward → equilibrium

The repeated oscillations allow energy to move through the medium.

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How Sound Is Produced

Sound begins with a vibrating source.

Examples include:

• a speaker cone
• vocal cords
• a tuning fork
• a guitar string
• a drum skin
• a vibrating machine

Consider a loudspeaker.

As the speaker cone moves outward, it pushes nearby air molecules closer together.

This produces a compression.

As the speaker cone moves inward, the nearby air molecules spread farther apart.

This produces a rarefaction.

Repeated vibrations produce a continuous series of compressions and rarefactions.

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How Sound Travels Through Air

When a vibrating object pushes nearby air particles, those particles collide and interact with neighbouring particles.

The disturbance passes from particle to particle.

A simplified sequence is:

1. A source vibrates.
2. Nearby air particles are pushed together.
3. A compression forms.
4. The particles transfer energy to neighbouring particles.
5. The source moves backward.
6. A rarefaction forms.
7. Repeated vibrations create alternating compressions and rarefactions.
8. The pattern travels through the air.

This travelling pressure disturbance is a sound wave.

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Sound Does Not Carry Air Across the Room

Suppose someone speaks from one side of a classroom.

The air molecules near the speaker's mouth do not travel across the entire room and enter the listener's ear.

Instead, each group of molecules moves a small distance backward and forward.

Energy is transferred from one group of particles to the next.

Therefore:

sound energy travels through the air

while:

air particles oscillate locally

This distinction is fundamental to understanding waves.

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Sound Requires a Medium

Sound is a mechanical wave.

Mechanical waves require matter through which to travel.

Sound can travel through:

• gases
• liquids
• solids

Sound cannot travel through a perfect vacuum because there are no particles available to transfer the disturbance.

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Sound in Space

Space is often described as silent because most of it is extremely close to a vacuum.

If two astronauts were floating outside a spacecraft with no air between them, shouting would not allow sound to travel directly through the vacuum.

However, they could communicate using radio waves.

Radio waves are electromagnetic waves and do not require a material medium.

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Sound Through Solids

Sound can also travel through solids.

If you place your ear against a table while someone taps the other end, vibrations travel through the material.

The particles in the solid vibrate around their equilibrium positions and transfer energy to neighbouring particles.

Sound often travels faster through solids than through gases because the particles are strongly coupled and disturbances can be transmitted efficiently.

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Sound Through Liquids

Sound also travels through liquids.

For example:

• whales communicate underwater
• sonar uses sound waves in water
• underwater microphones detect vibrations
• medical ultrasound travels through body tissues and fluids

The particles oscillate and transfer the pressure disturbance through the material.

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Wavelength in a Longitudinal Wave

Longitudinal waves have wavelength just as transverse waves do.

The wavelength, λ, is the distance between two corresponding points in consecutive wave cycles.

For a longitudinal wave, wavelength can be measured from:

centre of one compression → centre of next compression

or:

centre of one rarefaction → centre of next rarefaction

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Measuring Wavelength

Suppose consecutive compressions are separated by:

0.80 m

Then:

λ = 0.80 m

Suppose the distance from the first compression to the fourth compression is:

2.4 m

There are three complete wavelengths between them.

Therefore:

3λ = 2.4

λ = 2.4/3

λ = 0.80 m

Count the intervals between corresponding regions rather than simply counting the compressions.

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Compression to Rarefaction Distance

The distance from the centre of one compression to the centre of the neighbouring rarefaction is:

λ/2

For example, if:

λ = 1.2 m

then:

compression-to-neighbouring-rarefaction distance = 1.2/2

= 0.60 m

A compression and its neighbouring rarefaction are therefore separated by half a wavelength.

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Frequency

Frequency is the number of complete wave cycles passing a point each second.

Symbol:

f

Unit:

hertz (Hz)

For example:

f = 200 Hz

means 200 complete cycles occur each second.

For sound, frequency is closely related to our perception of pitch.

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Frequency and Pitch

Higher-frequency sound waves are generally heard as higher-pitched sounds.

Lower-frequency waves are heard as lower-pitched sounds.

For example:

• low frequency → low pitch
• high frequency → high pitch

Frequency and loudness are different properties.

A high-pitched sound does not necessarily have to be loud.

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Amplitude in Longitudinal Waves

Longitudinal waves also have amplitude, although it is not represented by a physical crest height.

Amplitude relates to the maximum disturbance of the particles or pressure from equilibrium.

For sound:

larger amplitude generally means larger pressure variations.

This is associated with a louder sound.

Therefore, in a simplified comparison:

greater sound-wave amplitude → greater sound intensity

and usually:

greater perceived loudness

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Compression Strength and Amplitude

A larger-amplitude longitudinal wave produces:

• more strongly compressed compressions
• more strongly spread rarefactions
• larger pressure variations

A smaller-amplitude wave produces smaller pressure variations.

The spacing between compressions, however, is related to wavelength rather than amplitude.

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Wave Speed

The basic wave equation applies to longitudinal waves:

v = fλ

where:

v = wave speed in m/s

f = frequency in Hz

λ = wavelength in m

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Worked Example

A sound wave has:

frequency = 250 Hz

wavelength = 1.36 m

Calculate its speed.

Use:

v = fλ

Substitute:

v = 250 × 1.36

v = 340 m/s

The sound wave travels at:

340 m/s

under the conditions represented by the data.

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Finding Wavelength

A sound wave travels at:

340 m/s

and has a frequency of:

500 Hz

Use:

v = fλ

Rearrange:

λ = v/f

Substitute:

λ = 340/500

λ = 0.68 m

The wavelength is:

0.68 m

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Finding Frequency

A longitudinal wave travels at:

300 m/s

with a wavelength of:

1.5 m

Use:

v = fλ

Rearrange:

f = v/λ

Substitute:

f = 300/1.5

f = 200 Hz

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Representing Longitudinal Waves

A longitudinal wave diagram may show particles as dots or vertical lines.

A compression appears as a crowded region:

||||||||

A rarefaction appears as a more widely spaced region:

| | | |

A simplified pattern might look like:

|||||||| | | | |||||||| | | | ||||||||

The crowded regions are compressions.

The spread-out regions are rarefactions.

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Reading a Longitudinal Wave Diagram

When examining a longitudinal wave diagram, ask:

1. Where are the particles closest together?
2. Where are they farthest apart?
3. Where is one compression?
4. Where is the next compression?
5. What distance represents one wavelength?
6. Which direction does the wave travel?
7. Which direction do the particles oscillate?

The key idea is:

particle motion is parallel to wave direction.

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Longitudinal Waves Can Be Drawn as Curves

Sometimes a longitudinal wave is represented using a graph that looks similar to a transverse wave.

This does not mean the particles are moving up and down.

For example, a sound-wave graph might show:

pressure vs position

A peak could represent:

high pressure → compression

A low point could represent:

low pressure → rarefaction

The vertical axis represents a measured quantity such as pressure, not necessarily physical vertical particle displacement.

This distinction is extremely important when interpreting wave diagrams.

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Pressure Graphs of Sound

Suppose a graph shows air pressure against position.

A region of maximum pressure corresponds approximately to a:

compression

A region of minimum pressure corresponds approximately to a:

rarefaction

The distance between consecutive pressure maxima represents:

one wavelength

Likewise, the distance between consecutive pressure minima represents one wavelength.

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Transverse Waves

In a transverse wave, particle motion is perpendicular to wave travel.

If the wave travels:

→

the particles might move:

↑ ↓

Examples include:

• waves on strings
• electromagnetic waves
• light
• S-waves from earthquakes

Transverse waves are commonly represented using crests and troughs.

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Longitudinal vs Transverse Waves

The most important difference is the direction of oscillation.

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What Longitudinal and Transverse Waves Have in Common

Despite their different particle motions, both types of waves:

• transfer energy
• can have wavelength
• can have frequency
• can have amplitude
• can have a period
• travel at a particular speed
• can be described using v = fλ
• involve oscillations

The main difference is the orientation of the oscillation.

---

Comparing Particle Motion

Suppose both waves travel to the right.

For a transverse wave:

wave →

particles ↑↓

For a longitudinal wave:

wave →

particles ↔

Therefore:

transverse → perpendicular

longitudinal → parallel

This is the most reliable way to classify the two types.

---

Sound from a Tuning Fork

A vibrating tuning fork demonstrates how vibrations produce sound.

As a prong moves outward, it pushes nearby air particles together.

A compression forms.

As the prong moves inward, a lower-pressure region forms.

A rarefaction develops.

Repeated vibration creates alternating compressions and rarefactions that move outward through the air.

---

From Source to Ear

When someone speaks:

1. Vocal cords vibrate.
2. The vibrations produce pressure changes in the air.
3. Compressions and rarefactions travel outward.
4. The sound wave reaches the ear.
5. The pressure variations cause the eardrum to vibrate.
6. The ear converts these vibrations into signals that can be interpreted by the brain.

Matter does not travel from the speaker's mouth all the way to the listener's ear.

The energy and disturbance travel.

---

Longitudinal Waves in Everyday Life

Longitudinal waves are involved in:

• speech
• music
• headphones and speakers
• microphones
• sonar
• ultrasound
• medical imaging
• seismic investigations
• machinery vibrations
• acoustic measurements

Understanding longitudinal waves therefore helps explain many familiar technologies.

---

Ultrasound

Ultrasound uses sound frequencies above the normal range of human hearing.

Ultrasound waves can travel through body tissues.

Reflections occur where the waves encounter boundaries between different materials or tissues.

The returning signals can be used to construct images.

The underlying wave travelling through the tissue is a mechanical pressure disturbance.

---

Sonar

Sonar uses sound waves to detect objects or determine distances underwater.

A sound pulse is sent through water.

It reflects from an object and returns.

By measuring the travel time, the distance can be estimated.

If the sound travels to an object and back:

distance to object = speed × total time / 2

The division by 2 is required because the sound travels the distance twice.

---

Seismic P-Waves

Earthquakes can produce P-waves.

P-waves are primarily longitudinal seismic waves.

Material oscillates approximately parallel to the direction the wave travels.

P-waves can travel through:

• solids
• liquids

They generally arrive at seismic stations before slower S-waves, which is why they are called primary waves.

---

Interpreting Spacing in Diagrams

Suppose a longitudinal-wave diagram contains compressions at:

x = 1 m

x = 4 m

x = 7 m

The spacing between consecutive compressions is:

4 − 1 = 3 m

and:

7 − 4 = 3 m

Therefore:

λ = 3 m

The diagram shows two complete wavelengths from the first compression to the third compression.

---

A Complete Example

A longitudinal wave travels through a spring.

Consecutive compressions are:

0.75 m apart

The frequency is:

6 Hz

Therefore:

λ = 0.75 m

Use:

v = fλ

v = 6 × 0.75

v = 4.5 m/s

If the wave travels horizontally along the spring, the coils oscillate horizontally backward and forward.

The wave is longitudinal because:

particle motion ∥ wave direction

---

Interpreting an Unfamiliar Diagram

When presented with an unfamiliar wave diagram, do not classify it only by its visual shape.

Instead:

1. Determine what the diagram represents.
2. Identify the direction of wave propagation.
3. Identify the direction of particle oscillation.
4. Locate high-density regions.
5. Locate low-density regions.
6. Identify corresponding points.
7. Measure wavelength between matching regions.
8. Check any axis labels and units.

A curved graph can represent a longitudinal wave if the vertical axis represents pressure, density, or displacement rather than the physical shape of the medium.

---

A Reliable Strategy for Identifying Longitudinal Waves

Ask these questions:

What is oscillating?

Particles of a medium.

Which direction do they oscillate?

Backward and forward.

Which direction does the wave travel?

Along the medium.

Are these directions parallel?

If yes, the wave is longitudinal.

Then identify:

crowded region → compression

spread-out region → rarefaction

---

Common Mistakes

Thinking particles travel through the medium with the sound

Particles oscillate locally while the disturbance transfers energy.

Thinking longitudinal particles move perpendicular to the wave

They move parallel to the wave direction.

Calling a compression a crest

Compressions belong to longitudinal waves. Crests describe transverse-wave displacement.

Calling a rarefaction a trough

A rarefaction is a low-density or low-pressure region, not a physical trough.

Measuring wavelength from compression to neighbouring rarefaction

That distance is approximately λ/2, not λ.

Counting compressions instead of intervals

Three consecutive compressions contain two complete wavelengths between the first and third.

Thinking sound can travel through empty space

Mechanical sound requires matter.

Assuming a curved wave graph must represent transverse motion

A curved graph might represent pressure or density in a longitudinal wave.

Confusing pitch and loudness

Frequency is associated with pitch.

Amplitude/intensity is associated with loudness.

Thinking frequency determines wave speed by itself

Wave speed depends strongly on the medium and its conditions. Frequency and wavelength are connected to that speed through v = fλ.

---

Key Terms

Longitudinal wave — wave in which particles oscillate parallel to the direction of wave travel.

Mechanical wave — wave that requires a material medium.

Medium — material through which a mechanical wave travels.

Particle — small constituent of matter that participates in the local oscillation of a mechanical wave.

Oscillation — repeated motion around an equilibrium position.

Equilibrium position — normal position around which particles oscillate.

Compression — region where particles are closer together than normal.

Rarefaction — region where particles are farther apart than normal.

Pressure — force per unit area; sound waves produce changing pressure in a medium.

Density — amount of mass per unit volume; compressions and rarefactions involve small changes in density.

Sound wave — mechanical wave produced by vibrations and transmitted through matter.

Wavelength (λ) — distance between corresponding points of consecutive wave cycles.

Frequency (f) — number of complete cycles per second, measured in hertz.

Period (T) — time required for one complete cycle.

Amplitude — maximum size of a disturbance from equilibrium.

Wave speed (v) — speed at which a disturbance propagates through a medium.

Pitch — perception associated mainly with sound frequency.

P-wave — primarily longitudinal seismic wave produced by an earthquake.

Ultrasound — sound with frequency above the normal human hearing range.

Sonar — technology using sound and its reflections to detect objects or determine distances.

---

Key Takeaways

• In a longitudinal wave, particle motion is parallel to the direction of wave travel.
• Particles oscillate around equilibrium rather than travelling with the wave.
• Longitudinal waves transfer energy through a medium.
• Compressions are regions where particles are closer together.
• Rarefactions are regions where particles are farther apart.
• A longitudinal wave contains alternating compressions and rarefactions.
• Sound in air is a longitudinal mechanical wave.
• A vibrating source produces changing pressure in the surrounding medium.
• Sound can travel through gases, liquids, and solids.
• Sound cannot travel through a perfect vacuum because there are no particles to transmit the mechanical disturbance.
• Wavelength can be measured from compression to compression or rarefaction to rarefaction.
• The distance from a compression to its neighbouring rarefaction is approximately half a wavelength.
• Frequency is the number of cycles per second.
• Higher sound frequency generally corresponds to higher pitch.
• Greater sound-wave amplitude is associated with larger pressure variations and generally greater intensity.
• Longitudinal waves obey v = fλ.
• A curved representation of a sound wave does not necessarily show particles moving vertically.
• Graphs may represent pressure, density, or displacement.
• Transverse waves have perpendicular oscillations; longitudinal waves have parallel oscillations.
• P-waves are important examples of longitudinal seismic waves.
• The most reliable way to identify a longitudinal wave is to compare the direction of particle oscillation with the direction of wave travel.

---

Check Your Understanding

1. Define a longitudinal wave in terms of particle motion and wave direction.
2. Explain what happens to particles of a medium as a longitudinal wave passes.
3. Define compression and rarefaction.
4. A spring contains alternating crowded and spread-out regions. Explain which regions represent compressions and which represent rarefactions.
5. Explain how the vibration of a speaker produces a sound wave in air.
6. Explain why sound cannot travel through a perfect vacuum.
7. Consecutive compressions are 1.5 m apart. Determine the wavelength.
8. The distance from the first compression to the fifth compression is 8 m. Determine the wavelength.
9. A longitudinal wave has a frequency of 12 Hz and wavelength of 2.5 m. Calculate its speed.
10. A sound wave travels at 340 m/s and has a frequency of 680 Hz. Calculate its wavelength.
11. Compare transverse and longitudinal waves in terms of particle motion, wave direction, and characteristic features.
12. A student sees a curved graph of a sound wave and concludes that the air particles must move vertically up and down. Explain why this conclusion may be incorrect.
13. A longitudinal-wave diagram shows compressions at x = 2 m, 5 m, 8 m, and 11 m. Determine the wavelength and the number of complete wavelengths between the first and fourth compressions.
14. Explain how sound can travel from a speaker to a listener even though individual air molecules do not travel across the room.
15. Sketch a longitudinal wave containing at least three compressions and three rarefactions. Identify the compressions, rarefactions, one wavelength, the direction of wave travel, and the direction of particle motion.

Seismic Waves

Seismic waves are waves of energy that travel through Earth or along its surface. They are produced when energy stored in rocks is suddenly released, most commonly during an earthquake.

Earthquakes can generate several types of seismic waves. The two most important waves that travel through Earth's interior are:

• P-waves — Primary waves
• S-waves — Secondary waves

These waves behave differently because they involve different types of particle motion.

Most importantly:

P-waves can travel through solids and liquids.

S-waves can travel through solids but not through liquids.

This difference has provided scientists with some of the strongest evidence about the structure of Earth's interior.

---

How Earthquakes Begin

Earth's crust is divided into large sections called tectonic plates.

These plates move slowly because of processes occurring within Earth.

Where plates interact, rocks can become:

• compressed
• stretched
• bent
• sheared

Friction can prevent rocks on opposite sides of a fault from moving smoothly.

As plate movement continues, stress builds in the rocks.

Eventually, the stress may become greater than the strength of the rocks or the friction holding them in place.

The rocks suddenly move.

This produces an earthquake.

---

Elastic Energy in Rocks

Rocks can deform slightly when forces act on them.

As stress builds, elastic potential energy can be stored in the rocks.

When the rocks suddenly fracture or slip along a fault, some of this stored energy is released.

The energy travels away from the earthquake source as:

seismic waves

This process is often described using the idea of elastic rebound.

---

The Focus

The point inside Earth where an earthquake begins is called the focus or hypocentre.

This is where the sudden movement and energy release originate.

Seismic waves spread outward from the focus in many directions.

The focus may be:

• shallow
• intermediate in depth
• deep

depending on the tectonic setting.

---

The Epicentre

The epicentre is the point on Earth's surface directly above the focus.

Therefore:

focus → inside Earth

epicentre → Earth's surface

These terms should not be confused.

---

Types of Seismic Waves

Seismic waves can be divided into two broad groups:

Body waves

These travel through Earth's interior.

They include:

• P-waves
• S-waves

Surface waves

These travel mainly along Earth's surface.

Important surface waves include:

• Love waves
• Rayleigh waves

P-waves and S-waves are particularly important for studying Earth's internal structure.

---

P-Waves

P-wave stands for Primary wave.

They are called primary waves because they are the fastest major seismic waves and therefore normally arrive first at a seismic station after an earthquake.

P-waves are longitudinal waves.

Particle motion occurs approximately parallel to the direction in which the wave travels.

If the P-wave travels:

→

particles vibrate:

↔

This produces alternating regions of compression and expansion.

---

Particle Motion in a P-Wave

Imagine pushing and pulling one end of a spring.

A region of compressed coils travels along the spring.

The coils themselves move backward and forward.

This provides a useful model of a P-wave.

In Earth:

• particles are pushed together
• particles move apart
• the compression disturbance travels forward

P-waves are therefore sometimes called compressional waves.

---

P-Waves Through Matter

P-waves can travel through:

• solids
• liquids
• gases

They can do this because compression and expansion can be transmitted through all of these states of matter.

For studying Earth, the important fact is:

P-waves can travel through both the solid mantle and the liquid outer core.

Their speed and direction change as they enter materials with different physical properties.

---

S-Waves

S-wave stands for Secondary wave.

S-waves travel more slowly than P-waves, so they normally arrive later at a seismic station.

S-waves are transverse waves.

Particle motion is perpendicular to the direction of wave travel.

If the S-wave travels:

→

particles might move:

↑ ↓

S-waves are also called shear waves.

---

Particle Motion in an S-Wave

Imagine shaking one end of a rope vertically.

The disturbance travels horizontally while pieces of rope move vertically.

This resembles the basic motion of an S-wave.

The material is displaced sideways relative to the direction in which the wave travels.

Therefore:

particle motion ⟂ wave direction

---

S-Waves Through Matter

S-waves can travel through:

solids

but they cannot travel through:

liquids

A liquid cannot support the type of shear deformation required to transmit an S-wave through its bulk.

This fact is extremely important.

Scientists discovered that S-waves produced by earthquakes do not travel through Earth's outer core.

This provided evidence that:

Earth's outer core is liquid.

---

Comparing P-Waves and S-Waves

A useful memory aid is:

P = Primary, Pressure, Passes through liquids

S = Secondary, Shear, Stops at liquids

---

Why P-Waves Are Faster

P-waves and S-waves deform materials differently.

P-waves involve compression and expansion.

S-waves involve shear deformation.

Under the same conditions, the properties of Earth materials allow compressional disturbances to travel faster than shear disturbances.

Therefore:

P-waves arrive before S-waves.

This difference in arrival time is useful for locating earthquakes.

---

Surface Waves

Not all seismic waves travel through Earth's interior.

Surface waves travel primarily along or near Earth's surface.

They are generally slower than P- and S-waves but can produce large ground motions.

Two important types are:

• Love waves
• Rayleigh waves

Surface waves can be particularly destructive during earthquakes.

---

Love Waves

Love waves move the ground from side to side.

Their particle motion is primarily horizontal and perpendicular to the direction of wave travel.

They can produce strong horizontal shaking.

This can place large stresses on:

• buildings
• bridges
• roads
• foundations

---

Rayleigh Waves

Rayleigh waves produce a rolling motion.

Particles move in approximately elliptical paths.

The motion can resemble waves rolling across the surface of water.

Rayleigh waves can produce both:

• vertical motion
• horizontal motion

This rolling ground motion can be particularly noticeable during large earthquakes.

---

Comparing the Major Seismic Waves

Different seismic waves therefore provide different information and produce different types of ground motion.

---

Detecting Seismic Waves

Seismic waves can be detected using instruments called seismometers.

A recording produced by seismic instruments is called a seismogram.

A seismogram can show the arrival of different types of seismic waves.

Because P-waves travel faster:

P-wave arrival occurs first

followed by:

S-wave arrival

and then often:

larger surface-wave motion

---

Reading a Seismogram

A simplified seismogram might show:

small early signal → P-wave

later signal → S-wave

larger later motion → surface waves

Scientists examine:

• arrival times
• wave amplitudes
• wave frequencies
• differences between P- and S-wave arrival times

These measurements provide information about the earthquake and Earth's interior.

---

The P–S Arrival-Time Difference

P-waves travel faster than S-waves.

Therefore, the farther a seismic station is from an earthquake, the greater the time difference between the arrival of the P-wave and the S-wave.

For example:

P-wave arrival: 10:15:20

S-wave arrival: 10:16:05

Difference:

45 seconds

This time difference can be compared with known seismic-wave travel information to estimate the station's distance from the earthquake.

---

Locating an Earthquake

One seismic station can estimate its distance from an earthquake, but it cannot usually determine the exact direction.

Data from several stations can be combined.

A simplified method uses triangulation:

1. determine the earthquake distance from Station A
2. draw a circle around Station A
3. repeat for Stations B and C
4. identify the region where the distances intersect

This helps determine the earthquake's epicentre.

---

Seismic Waves and Earth's Interior

We cannot directly travel to most of Earth's interior.

Earth's radius is approximately:

6370 km

Even the deepest drilling reaches only a tiny fraction of this distance.

Scientists therefore rely on indirect evidence.

Seismic waves provide one of the most important ways of investigating the internal structure of Earth.

They act somewhat like a natural probe travelling through the planet.

---

Earth's Main Internal Layers

Earth can be divided into major layers:

• crust
• mantle
• outer core
• inner core

These layers have different:

• compositions
• densities
• temperatures
• pressures
• physical states

Seismic waves behave differently as they encounter these materials.

---

Seismic Wave Speed Changes

The speed of a seismic wave depends on the properties of the material through which it travels.

Important factors include:

• density
• rigidity
• compressibility
• physical state

As seismic waves move through different parts of Earth, their speeds change.

Scientists can analyze these changes to identify boundaries between internal layers.

---

Refraction Inside Earth

When a seismic wave enters a region where its speed changes, its direction can also change.

This is called refraction.

The same general wave phenomenon occurs with:

• light
• water waves
• sound
• seismic waves

Because Earth's properties change with depth, seismic-wave paths through Earth are generally curved rather than perfectly straight.

---

Reflection Inside Earth

Some seismic-wave energy can also be reflected from boundaries inside Earth.

By studying reflected and refracted waves, scientists can infer:

• where boundaries occur
• how deep they are
• how material properties change

This is similar in principle to using echoes to investigate something that cannot be seen directly.

---

Evidence for the Liquid Outer Core

One of the most important discoveries from seismic waves concerns Earth's outer core.

Scientists observed that:

S-waves do not pass through the outer core.

Because S-waves cannot travel through liquids, this provides strong evidence that:

the outer core is liquid.

This is a powerful example of using wave behaviour to infer something that cannot be observed directly.

---

P-Waves and the Outer Core

P-waves can travel through liquids, so they do enter the outer core.

However, their speed changes dramatically at the mantle–outer-core boundary.

Their paths are strongly refracted.

This produces regions of Earth's surface where direct P-waves from a particular earthquake are not detected.

These regions contribute to the P-wave shadow zone.

---

The S-Wave Shadow Zone

Because S-waves cannot travel through the liquid outer core, there are large regions on the opposite side of Earth from an earthquake where direct S-waves are absent.

This is called the:

S-wave shadow zone

The existence of this shadow zone was crucial evidence for Earth's internal structure.

---

What Is a Shadow Zone?

A seismic shadow zone is a region of Earth's surface where particular direct seismic waves from an earthquake are not detected.

Shadow zones occur because seismic waves:

• change speed
• refract
• reflect
• may be unable to travel through certain materials

The pattern of these zones gives scientists information about Earth's internal layers.

---

Evidence for the Inner Core

P-wave behaviour provides evidence that Earth contains more than simply a mantle surrounding one uniform core.

Detailed seismic observations indicate that the centre of Earth contains a solid inner core surrounded by a liquid outer core.

The inner core remains solid despite its extremely high temperature because the pressure at Earth's centre is enormous.

---

Using Seismic Waves Like Medical Imaging

A useful analogy is medical imaging.

Doctors can investigate structures inside the body without opening it.

Similarly, geophysicists analyze waves travelling through Earth to infer structures they cannot directly see.

Modern seismic tomography uses seismic data from many earthquakes and stations to construct three-dimensional models of Earth's interior.

This can reveal regions where seismic waves travel slightly faster or slower.

---

What Seismic Tomography Can Show

Seismic tomography can provide evidence about:

• variations in mantle temperature
• subducting tectonic plates
• mantle structures
• boundaries between major layers
• regions with different physical properties

It is similar in concept to creating a three-dimensional image using many different wave paths.

---

Earthquake Magnitude and Wave Amplitude

Larger earthquakes generally release more energy and produce stronger seismic waves.

Seismometers record wave amplitude, which contributes to measurements used to characterize earthquakes.

However, the size of recorded waves at a station also depends on:

• distance from the earthquake
• local geology
• wave type
• depth of the earthquake
• direction of wave propagation

Therefore, a single observed amplitude should not be interpreted without context.

---

Seismic Waves and Earthquake Hazards

Different seismic waves can contribute to different types of ground motion.

Potential earthquake hazards include:

• building collapse
• bridge damage
• landslides
• liquefaction
• fires
• infrastructure failure
• tsunamis

The severity of shaking depends on much more than earthquake magnitude alone.

---

Local Geology and Shaking

The material beneath a location can influence how strongly the ground shakes.

Soft sediments can sometimes amplify seismic motion compared with solid bedrock.

Therefore, two places at similar distances from an earthquake may experience different levels of shaking.

Engineers use seismic information when designing structures in earthquake-prone regions.

---

Seismic Waves and Building Design

Engineers consider earthquake motion when designing:

• skyscrapers
• bridges
• hospitals
• dams
• transportation systems

Earthquake-resistant designs may use:

• flexible structures
• reinforced frames
• dampers
• base isolation systems

Understanding the frequencies and motions produced by seismic waves helps engineers reduce earthquake risk.

---

A Complete Comparison Example

Suppose an earthquake occurs and a seismic station records two body waves.

Wave A:

• arrives first
• particles oscillate parallel to wave direction
• can pass through the outer core

Wave B:

• arrives later
• particles oscillate perpendicular to wave direction
• disappears when it reaches the liquid outer core

Therefore:

Wave A = P-wave

Wave B = S-wave

The observations also provide evidence that:

Earth's outer core is liquid.

---

Interpreting a Seismic-Wave Diagram

When looking at a diagram, ask:

1. Which direction is the wave travelling?
2. Which direction are particles moving?
3. Is particle motion parallel or perpendicular?
4. Is the wave passing through solid material?
5. Is it passing through liquid?
6. Does its path bend at a boundary?
7. Is there a region where the wave is absent?
8. What does this reveal about Earth's interior?

These questions help turn a diagram into physical evidence.

---

Identifying P- and S-Waves from Motion

If particles move:

parallel to wave travel

identify the wave as:

P-wave

If particles move:

perpendicular to wave travel

identify the wave as:

S-wave

Remember:

P-wave → longitudinal

S-wave → transverse

---

Identifying P- and S-Waves from Materials

If a seismic wave travels through:

solid mantle → liquid outer core

it must be capable of travelling through liquid.

This points to a:

P-wave

If a wave travels through the solid mantle but does not pass through the liquid outer core:

S-wave

This reasoning is often used when interpreting diagrams of Earth's interior.

---

A Reliable Strategy for Comparing Seismic Waves

When comparing seismic waves, consider:

Wave type

Longitudinal, transverse, or surface.

Particle motion

Parallel, perpendicular, horizontal, or rolling.

Speed

Which arrives first?

Materials

Can it travel through solids? Liquids?

Path

Does it refract or reflect?

Evidence

What does its behaviour reveal about Earth's interior?

Effects

How does it contribute to ground motion?

This produces a more complete comparison than simply memorizing wave names.

---

Common Mistakes

Thinking P means "powerful"

P means Primary, referring to its earlier arrival.

Thinking S means "surface"

S means Secondary. S-waves are body waves, not surface waves.

Thinking S-waves travel through liquids

They do not propagate through Earth's liquid outer core.

Thinking P-waves only travel through solids

P-waves can travel through both solids and liquids.

Confusing P-wave motion with S-wave motion

P-wave particle motion is parallel.

S-wave particle motion is perpendicular.

Confusing the focus and epicentre

The focus is inside Earth.

The epicentre is directly above it at the surface.

Thinking seismic waves carry rocks across Earth

Particles vibrate locally while energy propagates through the material.

Thinking all seismic waves travel at the same speed

Different seismic-wave types travel at different speeds.

Thinking wave paths through Earth are always straight

Changing material properties cause refraction and curved paths.

Thinking the outer core was discovered by direct observation

Its liquid state is inferred from multiple lines of evidence, including seismic-wave behaviour.

Thinking surface waves are the fastest

P-waves are the fastest major seismic waves.

---

Key Terms

Seismic wave — wave of energy travelling through Earth or along its surface.

Earthquake — sudden release of stored energy caused by movement or fracture of rock.

Fault — fracture or zone of fractures along which rock movement can occur.

Elastic rebound — release of stored elastic energy when stressed rocks suddenly move.

Focus (hypocentre) — point inside Earth where an earthquake begins.

Epicentre — point on Earth's surface directly above the focus.

Body wave — seismic wave that travels through Earth's interior.

Surface wave — seismic wave travelling mainly along Earth's surface.

P-wave — fast longitudinal seismic body wave capable of travelling through solids and liquids.

S-wave — transverse seismic body wave that travels through solids but not liquids.

Compression — region where particles are pushed closer together.

Shear — deformation in which material is displaced sideways.

Love wave — surface wave producing mainly horizontal side-to-side motion.

Rayleigh wave — surface wave producing rolling or elliptical particle motion.

Seismometer — instrument used to detect and measure seismic motion.

Seismogram — recorded trace of seismic-wave motion.

Refraction — change in wave direction caused by a change in speed.

Reflection — return of wave energy from a boundary.

Shadow zone — region where particular direct seismic waves from an earthquake are not detected.

Outer core — liquid layer of Earth surrounding the inner core.

Inner core — solid central region of Earth.

Seismic tomography — technique using many seismic-wave paths to investigate Earth's internal structure.

---

Key Takeaways

• Earthquakes release stored energy that travels through Earth as seismic waves.
• The earthquake begins at the focus or hypocentre.
• The epicentre is the point on Earth's surface directly above the focus.
• P-waves and S-waves are body waves that travel through Earth's interior.
• P-waves are longitudinal waves.
• P-wave particle motion is parallel to the direction of wave travel.
• P-waves are faster than S-waves and normally arrive first.
• P-waves can travel through both solids and liquids.
• S-waves are transverse waves.
• S-wave particle motion is perpendicular to wave travel.
• S-waves travel through solids but not through liquids.
• The absence of S-waves through Earth's outer core provides strong evidence that the outer core is liquid.
• P-waves refract strongly when they enter the outer core.
• Refraction and the inability of S-waves to cross the outer core produce seismic shadow zones.
• Seismic-wave speeds change when material properties change.
• These changes reveal boundaries between Earth's internal layers.
• Seismic evidence supports a layered Earth containing a crust, mantle, liquid outer core, and solid inner core.
• P- and S-wave arrival-time differences can help determine distance from an earthquake.
• Measurements from multiple seismic stations can help locate an earthquake.
• Love and Rayleigh waves travel mainly along Earth's surface.
• Surface waves can produce strong and damaging ground motion.
• Seismometers detect seismic waves and produce seismograms.
• Seismic tomography uses large numbers of seismic observations to create models of Earth's interior.
• Seismic waves allow scientists to investigate regions of Earth that cannot be directly observed.
• Comparing how different waves travel through different materials is one of the most powerful ways to understand Earth's internal structure.

---

Check Your Understanding

1. Explain how an earthquake produces seismic waves.
2. Distinguish between the focus and the epicentre of an earthquake.
3. Describe the particle motion in a P-wave and identify whether it is longitudinal or transverse.
4. Describe the particle motion in an S-wave and identify whether it is longitudinal or transverse.
5. Which seismic body wave normally reaches a seismic station first? Explain why.
6. Complete the comparison: Which of P-waves and S-waves can travel through solids? Which can travel through liquids?
7. Explain why the absence of S-waves passing through Earth's outer core provides evidence that the outer core is liquid.
8. A seismic wave passes through the mantle and continues into the liquid outer core. Is it more likely to be a P-wave or an S-wave? Explain.
9. Compare P-waves and S-waves in terms of speed, particle motion, wave type, and the materials through which they can travel.
10. Explain why seismic-wave paths through Earth may bend rather than travel in perfectly straight lines.
11. A seismogram records a small signal first, another signal later, and large surface motion after that. Identify the likely P-wave, S-wave, and surface-wave arrivals.
12. Explain how the difference between P-wave and S-wave arrival times can help scientists determine the distance to an earthquake.
13. What is a seismic shadow zone, and what can shadow zones reveal about Earth's interior?
14. Compare P-waves, S-waves, Love waves, and Rayleigh waves. Include where they travel and the type of particle motion associated with each.
15. Scientists cannot directly travel through Earth's mantle and core. Explain how observations of P-waves, S-waves, changes in wave speed, refraction, and shadow zones provide evidence for a layered Earth containing a solid mantle, liquid outer core, and solid inner core.

Applications of Mechanical Waves

Mechanical waves transfer energy through matter. Unlike electromagnetic waves, mechanical waves require a medium such as a solid, liquid, or gas through which to travel.

Mechanical waves are involved in many technologies and everyday experiences, including:

• speech and hearing
• music
• medical ultrasound
• sonar
• earthquake detection
• engineering inspections
• noise control
• musical instruments
• ocean waves

Understanding properties such as frequency, wavelength, amplitude, speed, reflection, refraction, diffraction, and interference allows scientists and engineers to use mechanical waves to solve practical problems.

---

Mechanical Waves Need a Medium

A mechanical wave cannot travel without matter.

The medium might be:

• gas — sound travelling through air
• liquid — sonar travelling through seawater
• solid — seismic waves travelling through rock

Particles in the medium oscillate and transfer energy to neighbouring particles.

The particles do not normally travel all the way from the source to the receiver.

Instead:

matter oscillates locally while energy travels through the medium.

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Mechanical Waves in Everyday Life

Mechanical waves are constantly around us.

Examples include:

• sound from a conversation
• music from speakers
• vibrations in musical instruments
• ripples across water
• waves at a beach
• vibrations from machinery
• seismic waves from earthquakes
• ultrasound used in hospitals
• sonar used by ships

Many of these applications involve sound waves, which are mechanical waves.

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Sound Waves

Sound is produced by a vibrating source.

Examples include:

• vocal cords
• speaker cones
• guitar strings
• drum skins
• tuning forks
• engines

In air, sound travels mainly as a longitudinal wave consisting of alternating:

compressions and rarefactions

Air particles oscillate parallel to the direction of wave travel.

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Hearing

The human ear detects sound waves.

A simplified sequence is:

1. A source vibrates.
2. Sound waves travel through the air.
3. Sound enters the ear canal.
4. The sound causes the eardrum to vibrate.
5. Vibrations are transferred through tiny bones in the middle ear.
6. Vibrations reach the inner ear.
7. Sensory cells convert the vibrations into electrical signals.
8. Signals travel to the brain.

The brain interprets these signals as sound.

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Frequency and Pitch

The frequency of a sound wave is the number of complete vibrations occurring each second.

Frequency is measured in:

hertz (Hz)

Frequency is strongly related to pitch.

In general:

higher frequency → higher pitch

lower frequency → lower pitch

For example, a high musical note has a greater frequency than a low musical note.

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Amplitude and Sound

The amplitude of a sound wave is related to the size of the pressure disturbance.

Greater-amplitude sound waves generally have:

• greater intensity
• more energy passing through a given area
• greater perceived loudness, although human loudness perception is more complex than amplitude alone

Therefore:

amplitude and frequency describe different properties.

Frequency is mainly associated with pitch.

Amplitude is associated with the strength of the disturbance.

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Human Hearing

Young people with healthy hearing can typically detect frequencies roughly between:

20 Hz and 20 000 Hz

although the exact range varies among individuals and generally changes with age.

Sound below the normal human hearing range is called:

infrasound

Sound above it is called:

ultrasound

Humans cannot normally hear ultrasound, but it has many important applications.

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Ultrasound

Ultrasound is sound with a frequency above the upper limit of normal human hearing.

In many applications:

f > 20 000 Hz

Ultrasound is still a mechanical wave.

It therefore requires matter through which to travel.

Ultrasound can travel through:

• body tissues
• liquids
• solids

It cannot travel through a perfect vacuum.

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Medical Ultrasound

One of the best-known applications of ultrasound is medical imaging.

A device called a transducer sends high-frequency sound pulses into the body.

When these waves encounter boundaries between different tissues, some of the sound is reflected.

The returning waves are detected by the transducer.

A computer processes these echoes to produce an image.

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How an Ultrasound Image Is Produced

A simplified process is:

1. The transducer produces ultrasound pulses.
2. The waves travel into the body.
3. Some waves encounter boundaries between different tissues.
4. Part of the wave energy is reflected.
5. Reflected waves return to the transducer.
6. The equipment measures the return time and strength of the echoes.
7. A computer uses this information to construct an image.

The system therefore relies heavily on:

reflection of mechanical waves.

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Measuring Depth with Ultrasound

The time taken for an ultrasound pulse to return can be used to estimate the depth of a reflecting boundary.

Use:

distance = speed × time

But the measured time includes the journey:

transducer → object → transducer

Therefore:

depth = vt/2

where:

v = speed of sound in the tissue

t = total return time

The division by 2 is essential.

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Worked Ultrasound Example

Suppose an ultrasound pulse travels through tissue at:

1540 m/s

The echo returns after:

0.00010 s

Calculate the depth of the reflecting structure.

Use:

depth = vt/2

depth = (1540 × 0.00010)/2

depth = 0.154/2

depth = 0.077 m

or:

7.7 cm

The reflecting structure is approximately 7.7 cm beneath the transducer.

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Why Ultrasound Gel Is Used

During an ultrasound examination, gel is usually placed between the transducer and the skin.

Air gaps would cause strong reflection at the boundary and interfere with transmission of the ultrasound into the body.

The gel:

• removes most air gaps
• improves contact
• allows more ultrasound energy to enter the body

This is an example of wave physics directly influencing medical practice.

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Uses of Medical Ultrasound

Ultrasound can be used to investigate:

• pregnancy and fetal development
• the heart
• blood vessels
• kidneys
• liver
• muscles and tendons
• other soft tissues

Different ultrasound techniques are designed for different medical purposes.

---

Doppler Ultrasound

The Doppler effect is the change in observed frequency caused by relative motion between a wave source and an observer or reflecting object.

Medical Doppler ultrasound can use frequency changes in waves reflected from moving blood cells.

This can provide information about:

• blood-flow direction
• blood-flow speed
• circulation
• heart and blood-vessel function

The technology combines reflection with the Doppler effect.

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Advantages and Limitations of Medical Ultrasound

Some advantages include:

• real-time imaging
• no ionizing radiation
• portable equipment is possible
• useful for many soft tissues
• relatively rapid examinations

Some limitations include:

• air can strongly interfere with transmission
• bone can block or strongly reflect ultrasound
• image quality depends on the tissues being examined
• interpretation requires skill

No imaging technique is ideal for every situation.

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Sonar

Sonar stands for Sound Navigation and Ranging.

Sonar uses sound waves, usually in water, to:

• detect objects
• measure distances
• determine water depth
• map the seafloor
• locate underwater structures

Sonar works using the reflection of sound waves.

---

How Sonar Works

A basic sonar system works like this:

1. A transmitter produces a sound pulse.
2. The pulse travels through water.
3. The wave reaches an object or the seabed.
4. Some sound is reflected.
5. The reflected wave returns.
6. A receiver detects the echo.
7. The travel time is measured.
8. Distance is calculated.

Again:

distance to object = vt/2

because the sound makes a round trip.

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Worked Sonar Example

A ship sends a sound pulse toward the seabed.

The echo returns after:

2.0 s

Suppose the speed of sound in seawater is:

1500 m/s

Total distance travelled:

distance = vt

distance = 1500 × 2.0

distance = 3000 m

This includes the downward and upward journeys.

Therefore:

depth = 3000/2

depth = 1500 m

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Sonar Applications

Sonar can be used for:

• measuring ocean depth
• mapping the seafloor
• locating underwater objects
• navigation
• fish finding
• scientific research
• studying underwater geology

Some marine animals also use sound in ways similar to sonar.

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Echolocation

Animals such as bats and dolphins use echolocation.

They produce sounds and detect returning echoes.

The timing and properties of the echoes can provide information about:

• distance
• direction
• size
• movement
• sometimes surface characteristics

Echolocation is a natural example of applying sound-wave reflection.

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Sound Reflection and Echoes

An echo occurs when sound reflects from a surface and returns to the listener or detector.

Reflection is useful in:

• sonar
• ultrasound
• echolocation
• acoustic measurements

But reflection can also create problems.

For example, excessive reflections inside a room can make speech difficult to understand.

Engineers therefore sometimes want sound to reflect and sometimes want it to be absorbed.

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Acoustics

Acoustics is the study of sound and its behaviour.

Engineers and architects apply acoustics when designing:

• classrooms
• theatres
• concert halls
• recording studios
• cinemas
• offices
• transportation systems

They consider how sound:

• reflects
• absorbs
• diffracts
• interferes
• travels through different materials

---

Designing a Concert Hall

A concert hall should allow sound to reach the audience clearly.

Too much absorption can make music sound weak.

Too much reflection can create confusing echoes and excessive reverberation.

Engineers therefore select:

• room shape
• wall materials
• ceiling structures
• acoustic panels
• seating materials

to control how sound behaves.

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Reverberation

Reverberation occurs when reflected sound continues to be heard for a short time after the original sound is produced.

Some reverberation can improve music.

Too much reverberation can make:

• speech unclear
• recordings muddy
• classrooms difficult to understand

Acoustic engineers therefore try to control reverberation time.

---

Sound Absorption

Soft or porous materials can absorb some sound energy.

Examples include:

• carpets
• curtains
• acoustic foam
• upholstered seats
• specialized wall panels

When sound is absorbed, some of its energy is converted into other forms, mainly thermal energy within the material.

Sound-absorbing materials can reduce unwanted reflections.

---

Noise Control

Mechanical-wave principles are also used to reduce unwanted noise.

Possible strategies include:

• absorbing sound
• blocking transmission
• isolating vibrations
• changing surface shapes
• reducing vibration at the source
• using interference

Applications include:

• buildings
• vehicles
• factories
• aircraft
• machinery
• headphones

---

Active Noise Cancellation

Some headphones use active noise cancellation.

A microphone detects incoming noise.

The electronics produce another sound wave designed to interfere destructively with the unwanted sound.

When the waves combine appropriately:

positive pressure disturbance + negative pressure disturbance → reduced resulting disturbance

This is an application of wave interference.

It works particularly well for some steady, low-frequency sounds.

---

Resonance

Resonance occurs when a system is driven at or near one of its natural frequencies, producing a large response.

Examples include:

• musical instruments
• vibrating strings
• air columns
• bridges
• buildings
• machinery

Resonance can be useful or dangerous.

Musical instruments use resonance to strengthen desired sounds.

Engineers often design structures to avoid dangerous resonant vibrations.

---

Mechanical Waves in Musical Instruments

Musical instruments depend heavily on mechanical waves.

In a guitar:

• strings vibrate
• waves travel along the strings
• the body of the guitar vibrates
• surrounding air vibrates
• sound reaches the listener

In wind instruments:

• air columns vibrate

In drums:

• stretched membranes vibrate

The instrument's shape and materials influence which frequencies are strengthened.

---

Standing Waves

Reflections can combine with incoming waves to produce standing waves.

Standing waves contain positions called:

nodes — little or no displacement

antinodes — maximum displacement

Standing waves are important in:

• strings
• pipes
• musical instruments
• acoustic systems
• mechanical structures

Engineers must sometimes encourage standing waves and sometimes prevent them.

---

Mechanical Waves in Engineering

Engineers use mechanical waves to:

• inspect materials
• detect cracks
• measure thickness
• locate structural defects
• study vibrations
• reduce noise
• monitor machinery
• investigate earthquakes
• design buildings and bridges

Mechanical waves can provide information about structures without requiring them to be cut open or dismantled.

---

Ultrasonic Testing

Ultrasonic testing is a type of non-destructive testing.

High-frequency sound waves are sent into a material.

If the waves encounter:

• cracks
• voids
• boundaries
• defects

some energy may be reflected.

The returning signals can reveal the location of hidden defects.

---

Why Non-Destructive Testing Is Useful

Imagine checking a metal component inside an aircraft.

Cutting the component open to look for cracks would destroy it.

Ultrasonic testing can help inspect the component while leaving it intact.

This can be useful for:

• aircraft parts
• pipelines
• railway components
• bridges
• pressure vessels
• welded joints

Wave reflection provides information about structures that cannot easily be seen.

---

Vibration Monitoring

Machines contain moving parts that create mechanical vibrations.

Engineers can measure:

• vibration frequency
• amplitude
• changes over time

An unusual vibration pattern may indicate:

• imbalance
• loose components
• bearing wear
• misalignment
• structural damage

Monitoring waves and vibrations can therefore help identify problems before equipment fails.

---

Seismic Engineering

Buildings and bridges can be affected by seismic waves during earthquakes.

Engineers study:

• ground-motion frequency
• amplitude
• resonance
• damping
• wave transmission through soil

Structures can then be designed to reduce dangerous motion.

Techniques may include:

• flexible structural systems
• dampers
• reinforced frames
• base isolation

Wave science therefore contributes directly to earthquake-resistant design.

---

Damping

Damping reduces the amplitude of oscillations by removing energy from a vibrating system.

Damping is important in:

• vehicles
• buildings
• bridges
• machinery
• suspension systems

For example, shock absorbers reduce repeated vehicle oscillations after a wheel encounters a bump.

---

Waves in Vehicles

Mechanical waves and vibrations occur throughout vehicles.

Examples include:

• engine vibration
• tyre vibrations
• suspension oscillations
• sound in the passenger compartment
• vibration through the vehicle frame

Engineers try to control these waves to improve:

• comfort
• safety
• durability
• noise levels

---

Water Waves in Engineering

Water waves are also mechanical waves.

Engineers study them when designing:

• harbours
• breakwaters
• offshore platforms
• coastal defences
• ships
• wave-energy devices

Important wave behaviours include:

• reflection
• refraction
• diffraction
• interference

Understanding these processes helps engineers predict how waves will interact with structures.

---

Seismic Waves in Earth Science

Seismic waves are another major application of mechanical-wave principles.

P-waves and S-waves travel through Earth after earthquakes.

Their behaviour helps scientists investigate:

• Earth's mantle
• the liquid outer core
• the solid inner core
• internal boundaries
• earthquake locations

S-waves cannot travel through Earth's liquid outer core, providing important evidence about Earth's internal structure.

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Comparing Important Applications

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Using Travel Time to Measure Distance

Ultrasound and sonar use the same basic principle.

A pulse travels to an object and returns.

If:

v = wave speed

t = round-trip time

then:

distance to object = vt/2

This equation works because:

total distance = 2 × object distance

Therefore:

object distance = total distance/2

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Worked Engineering Example

An ultrasonic pulse travels through a metal component at:

5900 m/s

An echo from a defect returns after:

0.000020 s

Calculate the depth of the defect.

Use:

depth = vt/2

depth = (5900 × 0.000020)/2

depth = 0.118/2

depth = 0.059 m

or:

5.9 cm

The defect is approximately 5.9 cm below the surface.

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Reflection

Reflection occurs when a wave encounters a boundary and some of its energy returns.

Applications include:

• sonar
• ultrasound imaging
• echolocation
• ultrasonic testing

The time and strength of the reflected wave can reveal information about the reflecting object.

---

Refraction

Refraction occurs when a wave changes speed and direction as it enters a different medium or region.

Applications include:

• seismic studies
• medical ultrasound
• underwater acoustics
• engineering measurements

Engineers must account for refraction when waves pass through materials with different properties.

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Diffraction

Diffraction is the spreading of waves around obstacles or through openings.

Sound diffraction explains why you may hear someone even when you cannot see them directly around a doorway or corner.

Diffraction becomes particularly noticeable when the wavelength is similar to the size of the opening or obstacle.

Lower-frequency sounds have longer wavelengths and can often diffract around large obstacles more noticeably than higher-frequency sounds.

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Interference

Interference occurs when two or more waves overlap.

Their displacements combine.

Constructive interference produces a larger resulting disturbance.

Destructive interference produces a smaller resulting disturbance.

Applications include:

• active noise cancellation
• acoustic engineering
• vibration control

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The Doppler Effect

The Doppler effect occurs when there is relative motion between a wave source and an observer.

A familiar example is an approaching ambulance.

As it approaches:

observed frequency is higher

After it passes and moves away:

observed frequency is lower

This causes the familiar change in perceived pitch.

The Doppler effect is also used in medical and engineering applications.

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Everyday Mechanical Waves

Mechanical waves appear in many ordinary situations.

Talking

Vocal cords vibrate and produce sound waves.

Listening to music

Speakers vibrate and produce pressure waves in air.

Playing guitar

Waves form on strings and vibrations produce sound.

Swimming

Water waves move across the pool.

Driving

Mechanical vibrations travel through the vehicle.

Using headphones

Speaker components create sound waves near the ear.

Hearing thunder

Pressure waves from rapidly expanding air travel through the atmosphere.

Feeling an earthquake

Seismic waves produce ground motion.

Recognizing these examples helps connect wave theory with everyday experience.

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Choosing the Right Wave Principle

When analyzing an application, identify the physical principle being used.

Ask:

Does the wave bounce back?

→ reflection

Does it bend because its speed changes?

→ refraction

Does it spread around an obstacle?

→ diffraction

Do waves combine?

→ interference

Does a system respond strongly at a particular frequency?

→ resonance

Does observed frequency change because of motion?

→ Doppler effect

This approach is more useful than simply memorizing applications.

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A Complete Application Example

Suppose a research boat uses sonar.

The speed of sound in the water is:

1500 m/s

An echo returns from an underwater object after:

0.80 s

Calculate the distance to the object.

Use:

distance = vt/2

distance = (1500 × 0.80)/2

distance = 1200/2

distance = 600 m

The object is approximately:

600 m away

The physics involved includes:

• production of a mechanical wave
• transmission through water
• reflection from the object
• detection of the echo
• measurement of travel time
• calculation of distance

A single technology can therefore involve several wave principles.

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Evaluating Wave Technologies

Mechanical-wave technologies have strengths and limitations.

When evaluating an application, consider:

• accuracy
• range
• resolution
• safety
• cost
• material being investigated
• environmental conditions
• interference from other waves
• absorption of wave energy
• speed of the wave in the medium

For example, sonar may work extremely well underwater but is not designed to operate through empty space because sound requires a medium.

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A Reliable Strategy for Analyzing Mechanical-Wave Applications

When given an unfamiliar application:

1. Identify the source of the wave.
2. Identify the type of mechanical wave.
3. Identify the medium.
4. Determine what is vibrating.
5. Identify the wave property being measured.
6. Look for reflection, refraction, diffraction, interference, resonance, or the Doppler effect.
7. Determine whether travel time is being measured.
8. Use v = fλ if frequency, wavelength, or speed is involved.
9. Use distance = vt/2 for a reflected pulse when appropriate.
10. Interpret the result in context.
11. Consider limitations of the technology.

This strategy allows wave concepts to be applied to unfamiliar situations.

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Common Mistakes

Thinking mechanical waves can travel through a vacuum

Mechanical waves require a material medium.

Thinking sound carries air from the source to the listener

Air particles oscillate locally while energy travels.

Thinking ultrasound is electromagnetic radiation

Ultrasound is high-frequency sound and is a mechanical wave.

Thinking ultrasound means extremely loud sound

"Ultra" refers to frequency above normal human hearing, not loudness.

Forgetting to divide by 2 in echo calculations

The measured time normally includes the trip to the object and back.

Confusing pitch and loudness

Frequency is associated mainly with pitch. Amplitude/intensity is associated with loudness.

Confusing reflection and refraction

Reflection is the return of wave energy from a boundary. Refraction involves a change in direction associated with changing wave speed.

Assuming all reflected waves are unwanted

Reflection is essential to sonar, ultrasound imaging, and ultrasonic testing.

Assuming all reflection is useful

Too much reflection can create unwanted echoes and reverberation.

Thinking resonance is always harmful

Resonance is deliberately used in musical instruments but can be dangerous in structures and machinery.

Thinking wave technologies rely on only one wave property

Many technologies combine several principles, such as reflection, timing, frequency, and interference.

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Key Terms

Mechanical wave — wave that requires a material medium through which to travel.

Medium — material through which a mechanical wave propagates.

Sound wave — mechanical pressure wave produced by a vibrating source.

Ultrasound — sound with a frequency above the normal upper limit of human hearing.

Transducer — device that converts energy from one form into another; ultrasound transducers produce and detect sound waves.

Echo — reflected sound detected after the original sound.

Sonar — technology that uses sound transmission and reflection to detect objects or determine distances underwater.

Echolocation — use of emitted sounds and returning echoes to obtain information about surroundings.

Reflection — return of wave energy from a boundary.

Refraction — change in wave direction associated with a change in wave speed.

Diffraction — spreading of waves around obstacles or through openings.

Interference — combination of overlapping waves.

Constructive interference — interference that produces a larger resulting disturbance.

Destructive interference — interference that produces a smaller resulting disturbance.

Resonance — large response produced when a system is driven near one of its natural frequencies.

Standing wave — wave pattern produced by interference that contains nodes and antinodes.

Node — position of minimum displacement in a standing wave.

Antinode — position of maximum displacement in a standing wave.

Doppler effect — change in observed frequency due to relative motion.

Acoustics — study of sound and its behaviour.

Reverberation — persistence of sound due to repeated reflections.

Damping — reduction of oscillation amplitude through energy loss.

Non-destructive testing — inspection of a material or structure without damaging it.

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Key Takeaways

• Mechanical waves require matter through which to travel.
• Mechanical waves transfer energy while particles mainly oscillate around equilibrium positions.
• Sound is one of the most important mechanical waves in everyday life and technology.
• Sound in air is primarily a longitudinal pressure wave.
• Frequency is associated mainly with pitch.
• Wave amplitude and intensity are related to the strength of a sound.
• Ultrasound is sound with frequency above normal human hearing.
• Medical ultrasound uses reflected sound waves to investigate structures inside the body.
• Ultrasound does not use ionizing radiation.
• Ultrasound gel improves transmission by reducing problematic air gaps between the transducer and skin.
• Doppler ultrasound can provide information about moving blood.
• Sonar uses sound and echoes to detect underwater objects and measure distances.
• For a reflected pulse, distance = vt/2.
• Animals such as bats and dolphins use echolocation.
• Acoustic engineers control reflection, absorption, diffraction, interference, and reverberation.
• Active noise cancellation uses destructive interference.
• Resonance can strengthen useful vibrations or create dangerous ones.
• Standing waves are important in musical instruments and other vibrating systems.
• Ultrasonic testing can detect hidden defects without destroying a component.
• Vibration monitoring can help engineers detect developing problems in machinery.
• Seismic-wave principles help scientists study Earth and engineers design safer structures.
• Water-wave principles are important in coastal and marine engineering.
• Reflection, refraction, diffraction, interference, resonance, and the Doppler effect have important practical applications.
• Mechanical waves occur throughout everyday life, from conversation and music to transportation, medicine, engineering, and natural hazards.
• Understanding wave behaviour allows scientists and engineers to use mechanical waves as tools for communication, measurement, imaging, detection, monitoring, and design.

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Check Your Understanding

1. What makes a wave a mechanical wave?
2. Explain how sound travels from a speaker to a listener without the same air particles travelling across the entire room.
3. Explain the difference between frequency and amplitude in a sound wave and how each affects what we hear.
4. What is ultrasound, and why is it still classified as a mechanical wave?
5. Describe how reflected ultrasound waves can be used to create a medical image.
6. An ultrasound pulse travels through tissue at 1540 m/s and returns after 0.000080 s. Calculate the depth of the reflecting structure.
7. Explain why ultrasound gel is placed between an ultrasound transducer and the patient's skin.
8. Describe how Doppler ultrasound can provide information about blood flow.
9. Explain how sonar uses reflection and travel time to determine the distance to an underwater object.
10. A sonar pulse travels through seawater at 1500 m/s and returns from the seabed after 1.6 s. Calculate the water depth.
11. Explain how bats or dolphins use echolocation and identify the wave principle involved.
12. Describe how reflection, absorption, and reverberation influence the design of a concert hall or classroom.
13. Explain how destructive interference is used in active noise-cancelling headphones.
14. An ultrasonic inspection pulse travels through steel at 5900 m/s. An echo from a crack returns after 0.000030 s. Calculate the depth of the crack and explain why this technique is useful to engineers.
15. Choose one application of mechanical waves from medicine, sonar, music, earthquake engineering, coastal engineering, noise control, or material testing. Explain the type of wave involved, the medium through which it travels, at least two wave principles used, and how understanding those principles makes the technology useful.