1. What Are Waves?

Introduction

Waves are everywhere.

When you hear music, see light, watch ripples move across water, or use a mobile phone, you are observing the effects of waves.

Although waves can look very different from one another, they share an important property:

A wave transfers energy from one place to another without causing an overall transfer of matter.

Understanding waves allows us to explain sound, light, earthquakes, communication technology, ocean motion, and many other phenomena.

 

 

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What Is a Wave?

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

A disturbance is a change that causes particles or fields to move or oscillate.

For example, dropping a stone into still water creates a disturbance.

Ripples then travel outward from the point where the stone entered the water.

The ripples carry energy away from the disturbance.

 

 

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Waves Transfer Energy

One of the most important ideas about waves is that they transfer energy.

Imagine a floating leaf on the surface of a pond.

As a water wave passes:

• The leaf moves up and down.
• The wave continues travelling forward.
• The leaf remains approximately in the same location.

The water itself has not travelled across the pond with the wave.

Instead, energy has travelled through the water.

Energy Transfer vs Matter Transfer

Consider people performing a "stadium wave."

Each person:

• Stands up.
• Sits back down.
• Remains in approximately the same location.

However, the wave travels around the stadium.

This demonstrates an important principle:

The disturbance travels, but the particles do not travel with it overall.

 

 

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Particles in a Wave

In many waves, particles oscillate around a fixed or equilibrium position.

To oscillate means to move repeatedly back and forth.

For example, in a water wave, particles may move:

• Up
• Down
• Forward
• Backward

However, after the wave passes, the particles remain close to where they started.

The energy, rather than the matter, has been transferred.

What Creates a Wave?

Every wave requires a source of disturbance.

Something must initially provide energy to create the wave.

Examples include:

Without a disturbance, there is no wave.

Waves from Vibrations

Many waves begin with a vibration.

A vibration is a repeated back-and-forth movement.

For example, when a guitar string is plucked:

1. The string vibrates.
2. The vibrating string disturbs the surrounding air.
3. The disturbance travels through the air as a sound wave.
4. The wave reaches your ear.
5. Your brain interprets the signal as sound.

 

 

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Two Major Categories of Waves

Waves can be divided into two broad categories:

Mechanical Waves

Mechanical waves require a medium through which to travel.

Examples include:

• Sound waves.
• Water waves.
• Waves on strings.
• Seismic waves.

Electromagnetic Waves

Electromagnetic waves do not require a medium.

They can travel through empty space.

Examples include:

• Radio waves.
• Microwaves.
• Infrared radiation.
• Visible light.
• Ultraviolet radiation.
• X-rays.
• Gamma rays.

This is why sunlight can travel through the vacuum of space from the Sun to Earth.

 

 

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What Is a Medium?

A medium is the substance through which a mechanical wave travels.

A medium can be:

• Solid
• Liquid
• Gas

For example:

Sound can travel through:

• Air.
• Water.
• Metal.
• Wood.

However, sound cannot travel through a vacuum because there are no particles available to carry the vibration.

Transverse Waves

Waves can also be classified according to how the particles move relative to the direction of the wave.

In a transverse wave, the oscillations are perpendicular to the direction the wave travels.

For example, if a wave travels horizontally:

→

the particles may move:

↑↓

Examples include:

• Waves on a rope.
• Electromagnetic waves.
• Some seismic waves.

 

 

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Longitudinal Waves

In a longitudinal wave, particles oscillate parallel to the direction the wave travels.

Instead of crests and troughs, longitudinal waves contain:

• Compressions – regions where particles are close together.
• Rarefactions – regions where particles are farther apart.

Sound waves travelling through air are an important example.

 

 

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Comparing Transverse and Longitudinal Waves

Both types transfer energy without an overall transfer of matter.

Common Examples of Waves

Waves appear in many situations.

Water Waves

Transfer energy across the surface of water.

Sound Waves

Carry vibrations through materials such as air.

Light Waves

Electromagnetic waves that allow us to see.

Radio Waves

Carry information used in communication.

Seismic Waves

Travel through Earth during earthquakes.

 

 

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Waves in Everyday Technology

Modern technology depends heavily on waves.

For example:

• Mobile phones use radio and microwave frequencies.
• Wi-Fi uses radio-frequency electromagnetic waves.
• Radios receive radio waves.
• Microwave ovens use microwaves.
• Medical imaging can use ultrasound, X-rays, and radio waves.
• Remote controls often use infrared radiation.
• Fibre-optic cables transmit information using light.

Without our understanding of waves, modern communication technology would not exist.

Real-World Applications

 

 

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Knowledge of waves is important in:

• Telecommunications.
• Medicine.
• Music and acoustics.
• Astronomy.
• Earthquake monitoring.
• Radar.
• Sonar.
• Wireless networking.
• Satellite communication.

The study of waves connects many areas of physics and technology.

Worked Examples

Example 1

What does a wave transfer?

Answer:

A wave transfers energy from one place to another.

Example 2

Does a water wave carry water across an entire ocean?

Answer:

No. Water particles mainly oscillate around their positions while the wave energy travels through the water.

Example 3

What creates a sound wave?

Answer:

A vibrating object creates a disturbance in a medium, producing a sound wave.

Example 4

Which type of wave requires a medium?

Answer:

A mechanical wave.

Example 5

Is light a mechanical or electromagnetic wave?

Answer:

Light is an electromagnetic wave.

Example 6

Is sound usually transverse or longitudinal?

Answer:

Sound travelling through air is a longitudinal wave.

Did You Know?

Light from the Sun takes about 8 minutes and 20 seconds to reach Earth.

Because light is an electromagnetic wave, it can travel through the vacuum of space. Sound cannot do this, which means that despite what is sometimes shown in science-fiction movies, an explosion in space would be silent to a distant observer unless its effects reached them through matter.

Key Terms

Key Takeaways

• A wave is a disturbance that transfers energy from one place to another.
• Waves transfer energy without producing an overall transfer of matter.
• Every wave requires an initial source of disturbance.
• Mechanical waves require a medium, while electromagnetic waves can travel through a vacuum.
• Waves can also be classified as transverse or longitudinal, depending on the direction of oscillation.
• Water waves, sound, light, radio waves, and seismic waves are all examples of waves.
• Understanding waves is essential for explaining many natural phenomena and technologies, from earthquakes and music to mobile phones and satellite communication.

2. Wave Properties

Learning outcomes

• I can identify crests, troughs, compressions, and rarefactions.
• I can define amplitude, wavelength, frequency, and period.
• I can relate wave properties to wave diagrams.
• I can compare the properties of different waves.
• I can explain how amplitude affects wave energy.

Introduction

Waves can look very different, but they can all be described using a small number of important properties.

For example, a water wave may be tall or short, closely spaced or widely spaced, and may pass a point quickly or slowly. These differences can be described using quantities such as amplitude, wavelength, frequency, and period.

Understanding these properties allows us to compare waves and predict how they behave.

 

 

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Transverse Wave Features

A transverse wave has particles oscillating perpendicular to the direction in which the wave travels.

Important features include:

• Crest – the highest point of the wave.
• Trough – the lowest point of the wave.
• Equilibrium position – the resting or central position of the medium.

 

 

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Crest

The crest is the point of maximum upward displacement from the equilibrium position.

In a water wave, the crest is the top of the wave.

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Trough

The trough is the point of maximum downward displacement from the equilibrium position.

The distance between a crest and the equilibrium position is related to the wave's amplitude.

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Longitudinal Wave Features

A longitudinal wave has particles oscillating parallel to the direction the wave travels.

Instead of crests and troughs, longitudinal waves contain:

• Compressions
• Rarefactions

Sound waves in air are an important example.

 

 

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Compression

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

In a sound wave, compressions correspond to regions of higher air pressure.

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Rarefaction

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

In a sound wave, rarefactions correspond to regions of lower air pressure.

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Amplitude

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

For a transverse wave, amplitude is measured from:

• the equilibrium position to a crest, or
• the equilibrium position to a trough.

It is not measured from crest to trough.

 

 

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Amplitude and Energy

Amplitude is related to the amount of energy carried by a wave.

In general:

• Larger amplitude → more energy.
• Smaller amplitude → less energy.

For example:

A loud sound has a greater amplitude than a quiet sound.

Large ocean waves also carry more energy than small ripples.

For many waves, the energy carried increases approximately with the square of the amplitude, so doubling the amplitude can correspond to much more than double the energy.

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Wavelength

The wavelength is the distance between two corresponding points on consecutive waves.

The symbol for wavelength is:

λ

(the Greek letter lambda).

Wavelength is usually measured in:

• metres (m),
• centimetres (cm),
• nanometres (nm), depending on the type of wave.

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Measuring Wavelength

For a transverse wave, wavelength can be measured from:

• crest to crest,
• trough to trough.

For a longitudinal wave, wavelength can be measured from:

• compression to compression,
• rarefaction to rarefaction.

 

 

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Frequency

Frequency is the number of complete waves that pass a point each second.

The symbol is:

f

The SI unit of frequency is the hertz (Hz).

One hertz means:

1 Hz = 1 wave per second

Examples:

• 5 Hz = 5 waves each second.
• 100 Hz = 100 waves each second.
• 1000 Hz = 1000 waves each second.

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Period

The period is the time taken for one complete wave or oscillation.

The symbol is:

T

The SI unit is the second (s).

Frequency and period are closely related.

\( f = \frac{1}{T} \)

A high-frequency wave has a short period.

A low-frequency wave has a long period.

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Comparing Frequency and Period

Frequency	Period
Number of waves per second	Time for one wave
Measured in hertz (Hz)	Measured in seconds (s)
High frequency → short period	Long period → low frequency

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Wave Speed

Wave speed describes how quickly the disturbance travels through a medium or through space.

It depends on frequency and wavelength.

This relationship is important because changing frequency or wavelength may affect the other quantity when wave speed remains constant.

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Reading a Wave Diagram

When looking at a wave diagram, identify:

1. The equilibrium position.
2. The crests and troughs.
3. The amplitude.
4. The wavelength.
5. The direction of wave travel if shown.

A well-labelled diagram makes the important properties much easier to identify.

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Comparing Waves

Consider two waves travelling through the same medium.

Wave A

• Large amplitude.
• Long wavelength.
• Low frequency.

Wave B

• Small amplitude.
• Short wavelength.
• High frequency.

Wave A carries more energy if its amplitude is greater, while Wave B produces more oscillations each second.

 

 

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Wave Properties and Sound

Wave properties help explain what we hear.

Frequency and Pitch

• Higher frequency → higher pitch.
• Lower frequency → lower pitch.

Amplitude and Loudness

• Greater amplitude → louder sound.
• Smaller amplitude → quieter sound.

This is why different musical notes and volumes correspond to different sound-wave patterns.

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Wave Properties and Light

Different wavelengths and frequencies of visible light produce different colours.

For example:

• Red light has a longer wavelength.
• Violet light has a shorter wavelength.

All visible light is part of the much larger electromagnetic spectrum.

 

 

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Real-World Applications

Wave properties are important in many technologies.

 

 

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Applications include:

• Radio communication.
• Wi-Fi and mobile phones.
• Medical ultrasound.
• Music and acoustics.
• Seismology.
• Radar.
• Sonar.
• Fibre-optic communication.

Engineers often adjust wave frequency, wavelength, and amplitude to carry information or produce specific effects.

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Worked Examples

Example 1

What is the highest point of a transverse wave called?

Answer:

The crest.

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Example 2

What is the lowest point called?

Answer:

The trough.

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Example 3

What are the crowded regions in a longitudinal wave called?

Answer:

Compressions.

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Example 4

A wave passes a point 12 times each second.

What is its frequency?

Answer:

12 Hz

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Example 5

A wave has a frequency of 4 Hz.

What is its period?

\( T = \frac{1}{4} \)​

 

T = 0.25 s

Answer:

0.25 s

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Example 6

Two waves have the same wavelength and frequency, but Wave A has twice the amplitude of Wave B.

Which wave carries more energy?

Answer:

Wave A, because greater amplitude corresponds to greater wave energy.

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Did You Know?

Human hearing typically detects sound frequencies from about 20 Hz to 20,000 Hz, although the upper limit usually decreases with age. Dogs and some other animals can hear frequencies far above the range humans can detect.

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Key Terms

Term	Definition
Crest	The highest point of a transverse wave.
Trough	The lowest point of a transverse wave.
Compression	A region of a longitudinal wave where particles are close together.
Rarefaction	A region of a longitudinal wave where particles are farther apart.
Amplitude	Maximum displacement from the equilibrium position.
Wavelength	Distance between corresponding points on consecutive waves.
Frequency	Number of complete waves passing a point each second.
Hertz (Hz)	The SI unit of frequency; one hertz equals one cycle per second.
Period	Time taken for one complete wave or oscillation.
Equilibrium Position	The resting or central position around which particles oscillate.

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Key Takeaways

• Transverse waves contain crests and troughs, while longitudinal waves contain compressions and rarefactions.
• Amplitude measures the maximum displacement from equilibrium and is related to the energy carried by a wave.
• Wavelength is the distance between corresponding points on successive waves.
• Frequency is the number of waves passing a point each second.
• Period is the time required for one complete wave and is inversely related to frequency.
• Comparing amplitude, wavelength, frequency, and period allows us to describe and distinguish different waves.
• Understanding wave properties is essential for explaining sound, light, communication technology, and many other physical phenomena.

 

 

 

 

3. Wave Speed

Wave Speed

Waves transfer energy from one place to another. They can travel through materials, such as sound travelling through air or waves travelling along a rope, and some waves, such as electromagnetic waves, can also travel through a vacuum.

One of the most important quantities used to describe a wave is its wave speed. Wave speed tells us how quickly the disturbance or wave pattern travels from one location to another.

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Learning Targets

• I can define wave speed.
• I can use the wave equation v = λf.
• I can calculate wave speed, frequency, or wavelength.
• I can explain how wave speed depends on the medium.
• I can solve problems involving the wave equation.

What Is Wave Speed?

Wave speed is the distance travelled by a wave per unit time.

Like other speeds, it can be described using:

Speed = Distance / Time

The SI unit for wave speed is:

metres per second (m/s)

For example, if a wave travels 20 m in 4 s:

Wave speed = 20 / 4

Wave speed = 5 m/s

This means the wave pattern travels 5 metres every second.

Waves Transfer Energy

A wave transfers energy, but it does not normally transport matter from the source all the way to the destination.

Imagine producing waves along a rope.

The wave travels along the rope, but the individual sections of rope mainly move around their equilibrium positions.

Similarly, when a water wave moves across the surface of a pond, the water itself does not simply travel across the pond with the wave.

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Wave speed describes how quickly this disturbance and its energy travel.

The Wave Equation

Wave speed is connected to frequency and wavelength.

The relationship is:

v = λf

where:

• v = wave speed in metres per second (m/s)
• λ = wavelength in metres (m)
• f = frequency in hertz (Hz)

This is one of the most important equations in wave physics.

Understanding the Wave Equation

The wave equation makes sense if we think about what frequency and wavelength mean.

Suppose:

Wavelength = 3 m

and:

Frequency = 2 Hz

A frequency of 2 Hz means that two complete waves pass a point every second.

Each wave is 3 m long.

Therefore, in one second:

Distance travelled = 2 × 3 m

Distance travelled = 6 m

So:

Wave speed = 6 m/s

Using the equation:

v = λf

v = 3 × 2

v = 6 m/s

Wavelength

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

The symbol for wavelength is the Greek letter:

λ

pronounced lambda.

The SI unit is:

metre (m)

For a transverse wave, wavelength can be measured:

• Crest to crest
• Trough to trough
• Between any two equivalent points on consecutive waves

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For a longitudinal wave, wavelength can be measured:

• Compression to compression
• Rarefaction to rarefaction

Frequency

Frequency is the number of complete waves or oscillations passing a point each second.

The symbol is:

f

The unit is:

hertz (Hz)

For example:

5 Hz = 5 waves per second

100 Hz = 100 waves per second

1000 Hz = 1000 waves per second

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A higher frequency means that more complete waves pass a point each second.

Comparing Frequency and Wavelength

When waves travel through the same medium at the same wave speed, frequency and wavelength are inversely related.

If frequency increases:

Wavelength decreases

If frequency decreases:

Wavelength increases

This follows from:

v = λf

If v remains constant, increasing one of the other quantities requires the other to decrease.

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Rearranging the Wave Equation

We can use the wave equation to calculate three different quantities.

To calculate wave speed:

v = λf

To calculate wavelength:

λ = v / f

To calculate frequency:

f = v / λ

Before solving a problem, identify which quantity you are trying to find and choose the correct form of the equation.

Worked Example — Calculating Wave Speed

A wave has:

Wavelength = 4 m

Frequency = 3 Hz

Calculate its speed.

Use:

v = λf

Substitute:

v = 4 × 3

v = 12 m/s

Therefore:

Wave speed = 12 m/s

Worked Example — Calculating Frequency

A wave travels at:

20 m/s

and has a wavelength of:

5 m

Calculate its frequency.

Use:

f = v / λ

Substitute:

f = 20 / 5

f = 4 Hz

Therefore:

Frequency = 4 Hz

This means four complete waves pass a point every second.

Worked Example — Calculating Wavelength

A sound wave travels at:

340 m/s

and has a frequency of:

170 Hz

Calculate its wavelength.

Use:

λ = v / f

Substitute:

λ = 340 / 170

λ = 2 m

Therefore:

Wavelength = 2 m

Unit Conversions

Before using the wave equation, quantities should normally be converted into appropriate SI units.

Wavelength should usually be in:

metres (m)

Frequency should be in:

hertz (Hz)

Wave speed will then be in:

metres per second (m/s)

Useful conversions include:

1 km = 1000 m

1 cm = 0.01 m

1 mm = 0.001 m

1 kHz = 1000 Hz

1 MHz = 1,000,000 Hz

Worked Example — Converting Units

A wave has a wavelength of:

50 cm

and a frequency of:

8 Hz

First convert the wavelength:

50 cm = 0.50 m

Now use:

v = λf

v = 0.50 × 8

v = 4 m/s

Therefore:

Wave speed = 4 m/s

Converting the units first prevents a common calculation error.

Wave Speed and the Medium

The speed of a wave often depends on the medium through which it travels.

A medium is the material through which a wave travels.

Examples include:

• Air
• Water
• Steel
• Glass
• A rope
• A spring

The properties of the medium determine how quickly a disturbance can be transferred from one part of the material to another.

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Sound Waves and the Medium

Sound is a mechanical wave, meaning it requires a medium.

Sound travels by causing particles in the medium to vibrate.

The vibrations are passed from particle to particle.

Sound generally travels faster through solids than through liquids and faster through liquids than through gases, although the exact speed depends on the properties and conditions of the material.

Typical values are approximately:

These values can vary with temperature, pressure, composition, and other conditions.

Why Does Sound Travel at Different Speeds?

Wave speed depends on how the particles of the medium interact.

In solids, particles are strongly connected and disturbances can often be transmitted rapidly.

In gases, particles are much farther apart and the mechanical properties are very different.

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However, simply saying that particles are "closer together" is not a complete explanation.

The speed depends on properties such as the medium's:

• Elasticity
• Density
• Temperature

Different types of waves depend on different properties of their medium.

Waves on a String

The speed of a wave travelling along a string depends on properties of the string.

Two particularly important factors are:

• Tension
• Mass per unit length

Increasing the tension generally increases the wave speed.

A heavier string per unit length generally has a lower wave speed for the same tension.

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This can be observed by producing waves on ropes or strings with different tensions.

Electromagnetic Waves

Electromagnetic waves are different from mechanical waves because they do not require a material medium.

They can travel through a vacuum.

Examples include:

• Radio waves
• Microwaves
• Infrared
• Visible light
• Ultraviolet
• X-rays
• Gamma rays

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In a vacuum, all electromagnetic waves travel at approximately:

3.00 × 10⁸ m/s

This is the speed of light in a vacuum.

Light Travelling Through Materials

Although electromagnetic waves travel fastest in a vacuum, they travel more slowly through materials such as:

• Water
• Glass
• Plastic

When light passes from one material into another, its speed can change.

This change in speed is responsible for refraction.

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For example, light entering glass from air usually slows down and changes direction unless it enters perpendicular to the boundary.

What Happens When a Wave Enters a New Medium?

When a wave crosses into another medium, its frequency normally remains unchanged because the source still produces oscillations at the same rate.

However, the wave speed may change.

Because:

v = λf

if:

frequency stays constant

and:

wave speed changes

then:

wavelength must change

This is an important application of the wave equation.

Example — Wave Entering a Slower Medium

Suppose a wave has:

Frequency = 5 Hz

In Medium A:

Wave speed = 20 m/s

Therefore:

λ = v/f

λ = 20/5

λ = 4 m

The wave enters Medium B where its speed becomes:

10 m/s

The frequency remains:

5 Hz

Therefore:

λ = 10/5

λ = 2 m

So when the wave slows down:

Wavelength decreases from 4 m to 2 m

The frequency remains unchanged.

Reading Wave Diagrams

Wave diagrams often allow wavelength to be measured directly.

For a transverse wave, identify two neighbouring:

• Crests
• Troughs
• Equivalent zero-crossing points

The horizontal distance between them is one wavelength.

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Be careful not to confuse:

Amplitude with wavelength.

Amplitude is measured from the equilibrium position vertically to a crest or trough.

Wavelength is measured between corresponding points along the direction of wave travel.

Worked Example — Reading a Wave

Suppose a diagram shows four complete wavelengths occupying a distance of:

12 m

One wavelength is:

λ = 12 / 4

λ = 3 m

If the frequency is:

6 Hz

then:

v = λf

v = 3 × 6

v = 18 m/s

Therefore:

Wave speed = 18 m/s

Frequency, Wavelength, and Wave Speed

It is important to understand which quantities determine which.

For a wave travelling in a particular medium, the properties of the medium largely determine the wave speed.

The source determines the frequency.

The wavelength then adjusts according to:

v = λf

For example, if the source frequency increases while the wave remains in the same medium:

Frequency increases

Wave speed remains approximately constant

Wavelength decreases

This distinction is important when analyzing wave behaviour.

Worked Example — Changing Frequency

A wave travels along a rope at:

24 m/s

Initially, its frequency is:

4 Hz

Its wavelength is:

λ = 24/4

λ = 6 m

The source frequency increases to:

8 Hz

If the rope conditions remain unchanged, the wave speed remains:

24 m/s

The new wavelength is:

λ = 24/8

λ = 3 m

Therefore:

Frequency doubled

Wavelength halved

Wave speed remained unchanged

Wave Speed in Everyday Life

Wave speed is important in many technologies and natural phenomena.

Communication

Radio signals carry information over large distances.

Medical imaging

Ultrasound uses sound waves travelling through body tissues.

Earthquakes

Seismic waves travel at different speeds through Earth's interior.

Music

Sound waves travel through air from instruments to listeners.

Sonar

Sound waves travel through water and reflect from objects.

Fibre-optic communication

Light waves transmit information through optical fibres.

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Understanding wave speed allows scientists and engineers to calculate distances, locate objects, study materials, and transmit information.

Measuring Distance Using Waves

Wave speed can be used to determine distance.

Suppose a sound pulse travels toward an object and reflects back.

If we know:

• Wave speed
• Total travel time

we can calculate the total distance travelled.

However, the wave travels:

To the object + back again

Therefore:

Distance to object = Total wave distance / 2

This principle is used in:

• Sonar
• Ultrasound
• Echo sounding
• Some distance sensors

Worked Example — Sonar

A sonar pulse travels through water at:

1500 m/s

The echo returns after:

0.40 s

First calculate the total distance travelled:

Distance = speed × time

Distance = 1500 × 0.40

Distance = 600 m

But this includes the journey to the object and back.

Therefore:

Distance to object = 600 / 2

Distance to object = 300 m

Common Mistakes

Mistake: Confusing wave speed with frequency

Wave speed is measured in:

m/s

Frequency is measured in:

Hz

They describe different properties.

Mistake: Confusing wavelength with amplitude

Wavelength is measured along the direction of wave travel.

Amplitude measures maximum displacement from equilibrium.

Mistake: Using centimetres directly in the wave equation

Convert centimetres to metres when SI units are required.

For example:

25 cm = 0.25 m

Mistake: Assuming higher frequency always means higher wave speed

In the same medium, changing frequency does not necessarily change wave speed.

Instead, wavelength often changes.

Mistake: Thinking frequency changes when a wave crosses a boundary

The frequency normally remains unchanged because it is determined by the source.

Wave speed and wavelength can change.

Mistake: Assuming all waves travel at the same speed

Wave speed depends on the type of wave and the medium through which it travels.

Mistake: Using the wrong form of the equation

Remember:

v = λf

λ = v/f

f = v/λ

Key Terms

Wave speed – the distance travelled by a wave per unit time.

Wavelength – the distance between equivalent points on consecutive waves.

Frequency – the number of complete oscillations or waves passing a point each second.

Hertz (Hz) – the unit of frequency; one hertz means one cycle per second.

Medium – a material through which a mechanical wave travels.

Mechanical wave – a wave that requires a material medium.

Electromagnetic wave – a wave that can travel through a vacuum.

Amplitude – the maximum displacement from the equilibrium position.

Refraction – a change in direction caused by a change in wave speed when a wave enters another medium at an angle.

Check Your Understanding

1. Define wave speed.

2. State the wave equation and identify each quantity.

3. What is the SI unit of wave speed?

4. A wave has a wavelength of 5 m and a frequency of 4 Hz. Calculate its speed.

5. A wave travels at 30 m/s and has a wavelength of 6 m. Calculate its frequency.

6. A wave travels at 200 m/s and has a frequency of 50 Hz. Calculate its wavelength.

7. Convert 75 cm into metres.

8. A wave has a wavelength of 75 cm and a frequency of 12 Hz. Calculate its wave speed.

9. Explain why the speed of a mechanical wave can change when it enters a different medium.

10. A wave enters a new medium and slows down. Its frequency remains constant. What happens to its wavelength?

11. Explain why increasing the frequency of a wave on the same rope does not necessarily increase its wave speed.

12. A sonar pulse travels through water at 1500 m/s and returns after 0.20 s. Calculate the distance to the reflecting object.

Key Takeaways

• Wave speed describes how quickly a wave disturbance travels.
• Wave speed is measured in metres per second (m/s).
• The wave equation connects wave speed, wavelength, and frequency: v = λf.
• Wavelength is measured in metres.
• Frequency is measured in hertz.
• The wave equation can be rearranged to calculate wave speed, wavelength, or frequency.
• Unit conversions should be completed before substituting values into calculations.
• Mechanical wave speed depends on the properties of the medium.
• Sound travels at different speeds through gases, liquids, and solids.
• Electromagnetic waves travel at approximately 3.00 × 10⁸ m/s in a vacuum.
• When a wave enters a different medium, its speed and wavelength can change while its frequency remains constant.
• In a particular medium with constant wave speed, increasing frequency results in a shorter wavelength.
• Wave-speed calculations have practical applications in sound, communications, sonar, ultrasound, seismology, and optics.

Did You Know?

Scientists can use the speeds of seismic waves to investigate Earth's interior. Because different seismic waves travel at different speeds and behave differently as they pass through Earth's layers, their arrival times provide evidence about structures deep beneath the surface that humans cannot observe directly.

4. Representing Waves

Representing Waves

Waves are constantly changing with both position and time, so physicists use graphs to represent them clearly. Two of the most important representations are displacement-distance graphs and displacement-time graphs.

These graphs may look very similar, but they show different information. Understanding which graph you are looking at is essential when finding quantities such as wavelength, period, frequency, and amplitude.

6

Learning Targets

• I can interpret displacement-distance graphs.
• I can interpret displacement-time graphs.
• I can distinguish between spatial and temporal wave graphs.
• I can determine wavelength and period from graphs.
• I can sketch simple wave diagrams.

---

Why Do We Use Wave Graphs?

A travelling wave involves many particles or points behaving differently at different positions and times.

Trying to describe all of this using words would be difficult.

Graphs allow us to represent important wave properties such as:

• Displacement
• Amplitude
• Wavelength
• Period
• Frequency

However, we need to pay close attention to the horizontal axis.

A wave graph with distance on the horizontal axis represents something different from a wave graph with time on the horizontal axis.

---

Displacement

Displacement describes how far a point in the medium has moved from its equilibrium position.

The equilibrium position is the position the point would occupy if no wave were passing through it.

Displacement can be:

• Positive
• Zero
• Negative

For a transverse wave:

• A crest represents maximum positive displacement.
• A trough represents maximum negative displacement.
• The centre line represents zero displacement.

4

---

Amplitude

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

It is measured from:

Equilibrium → Crest

or:

Equilibrium → Trough

It is not measured from the trough to the crest.

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

Amplitude = 8 / 2

Amplitude = 4 cm

4

---

Displacement-Distance Graphs

A displacement-distance graph shows the shape of a wave at a particular instant in time.

The vertical axis represents:

Displacement

The horizontal axis represents:

Distance

This is sometimes called a spatial wave graph because it shows how displacement varies with position in space.

Think of it as taking a photograph of the wave at one instant.

4

---

Reading a Displacement-Distance Graph

A displacement-distance graph can tell us:

• The displacement at different positions
• The amplitude
• The wavelength
• The shape of the wave at that instant

Suppose the graph shows crests at:

x = 2 m

and:

x = 8 m

The wavelength is the distance between the two neighbouring crests:

λ = 8 − 2

λ = 6 m

Therefore:

Wavelength = 6 m

---

Finding Wavelength

Wavelength is the distance between two consecutive points that are at the same stage of a wave cycle.

The symbol is:

λ

Wavelength can be measured:

Crest → next crest

Trough → next trough

or between any other two consecutive equivalent points.

5

Wavelength is a distance, so its SI unit is:

metre (m)

---

Worked Example — Finding Wavelength

A displacement-distance graph has one crest at:

x = 1.5 m

and the next crest at:

x = 5.5 m

Calculate the wavelength.

λ = 5.5 − 1.5

λ = 4.0 m

Therefore:

Wavelength = 4.0 m

Notice that no time information was required.

The horizontal axis represents distance.

---

Displacement-Time Graphs

A displacement-time graph shows how the displacement of one particular point changes as time passes.

The vertical axis represents:

Displacement

The horizontal axis represents:

Time

This is sometimes called a temporal wave graph.

5

Instead of showing the entire wave at one moment, this graph follows one position over time.

---

Imagine a Floating Cork

Imagine a cork floating on water while waves pass underneath it.

The cork moves:

Up → equilibrium → down → equilibrium → up

repeatedly.

If we recorded the vertical displacement of the cork over time, we could draw a displacement-time graph.

The graph describes the oscillation of the cork at one location.

It does not directly show the physical shape of the entire water wave.

4

---

Period

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

The symbol is:

T

The SI unit is:

second (s)

On a displacement-time graph, the period can be measured from:

One crest → next crest

or:

One trough → next trough

or between any two consecutive equivalent points.

---

Worked Example — Finding Period

Suppose one crest occurs at:

t = 1 s

and the next crest occurs at:

t = 5 s

Then:

T = 5 − 1

T = 4 s

Therefore:

Period = 4 s

This means one complete oscillation takes four seconds.

---

Period and Frequency

Period and frequency are closely related.

Frequency tells us how many oscillations occur each second.

Period tells us how long one oscillation takes.

Therefore:

f = 1 / T

and:

T = 1 / f

For example, if:

T = 0.25 s

then:

f = 1 / 0.25

f = 4 Hz

Four complete oscillations occur every second.

---

Worked Example — Finding Frequency from a Graph

A displacement-time graph shows that one complete oscillation takes:

0.20 s

Therefore:

T = 0.20 s

Use:

f = 1 / T

f = 1 / 0.20

f = 5 Hz

Therefore:

Frequency = 5 Hz

---

Spatial vs Temporal Wave Graphs

This distinction is extremely important.

Displacement-Distance Graph	Displacement-Time Graph
Horizontal axis = distance	Horizontal axis = time
Shows many positions	Shows one position over time
Snapshot of the wave	Record of an oscillating point
Used to find wavelength	Used to find period
Spatial representation	Temporal representation
Horizontal unit usually m	Horizontal unit usually s

The graphs may have very similar shapes.

Always check the horizontal axis before interpreting the graph.

---

A Useful Way to Remember

Think of the two graphs this way:

Displacement-Distance

A photograph

You see the wave at one instant across many positions.

Displacement-Time

A video of one point

You watch how one location moves as time passes.

This distinction prevents many common errors.

---

Same Wave, Different Graphs

A single travelling wave can be represented using both types of graph.

Suppose a wave has:

Wavelength = 4 m

Frequency = 2 Hz

Its period is:

T = 1/f

T = 1/2

T = 0.5 s

A displacement-distance graph would repeat every:

4 m

A displacement-time graph would repeat every:

0.5 s

4

These represent the same wave but describe it in different ways.

---

Connecting the Two Graphs

The wave equation connects the spatial and temporal descriptions:

v = λf

Because:

f = 1/T

we can also write:

v = λ/T

This makes physical sense.

During one period, a travelling wave moves forward by one wavelength.

Therefore:

Wave speed = One wavelength / One period

---

Worked Example — Using Both Graphs

A displacement-distance graph gives:

λ = 3 m

A displacement-time graph for the same wave gives:

T = 0.50 s

First calculate frequency:

f = 1/T

f = 1/0.50

f = 2 Hz

Now calculate wave speed:

v = λf

v = 3 × 2

v = 6 m/s

Therefore:

Wave speed = 6 m/s

---

Determining Amplitude from Either Graph

Amplitude can be determined from either a displacement-distance graph or a displacement-time graph.

Suppose the vertical axis shows:

Maximum displacement = +0.30 m

Minimum displacement = −0.30 m

The amplitude is:

0.30 m

Do not calculate:

0.30 − (−0.30) = 0.60 m

That is the total crest-to-trough displacement, not the amplitude.

---

Reading Points on a Displacement-Distance Graph

Suppose a displacement-distance graph shows a point at:

x = 3 m

with displacement:

+0.20 m

This means:

At the instant represented by the graph, the point in the medium located 3 m from the origin is displaced 0.20 m in the positive direction.

It does not mean that the point travelled 3 m.

The horizontal coordinate describes its position in the medium.

---

Reading Points on a Displacement-Time Graph

Suppose a displacement-time graph shows:

At:

t = 3 s

the displacement is:

−0.10 m

This means that after 3 seconds, the particular point being observed is displaced 0.10 m in the negative direction from equilibrium.

The horizontal coordinate is now time, not position.

---

Sketching a Simple Wave

To sketch a wave accurately:

• Draw and label the horizontal axis.
• Draw and label the vertical displacement axis.
• Mark the equilibrium position.
• Draw smooth crests and troughs.
• Show a consistent wavelength or period if the wave is periodic.
• Label important quantities.

5

A wave should normally be drawn as a smooth curve rather than as a series of sharp triangles.

---

Sketching a Displacement-Distance Graph

Suppose you are told:

Amplitude = 2 cm

Wavelength = 4 m

Your graph should:

• Have displacement on the vertical axis.
• Have distance on the horizontal axis.
• Reach +2 cm at the crests.
• Reach −2 cm at the troughs.
• Repeat every 4 m.

The distance between neighbouring crests should therefore be:

4 m

---

Sketching a Displacement-Time Graph

Suppose:

Amplitude = 3 cm

Period = 2 s

Your graph should:

• Have displacement on the vertical axis.
• Have time on the horizontal axis.
• Reach +3 cm at maximum positive displacement.
• Reach −3 cm at maximum negative displacement.
• Repeat every 2 s.

The time between neighbouring crests should therefore be:

2 s

---

Wave Direction

A single displacement-distance graph shows the shape of the wave at one instant, but it does not necessarily tell us which direction the wave is travelling.

5

The same wave shape could potentially be moving:

Left

or:

Right

Additional information is required, such as:

• A second graph taken slightly later.
• An arrow showing the direction of propagation.
• Information about how a particular point is moving.

This is an important limitation of a single spatial graph.

---

Successive Wave Snapshots

Imagine taking two photographs of a travelling wave separated by a short time.

In the first image, a crest is at:

x = 2 m

A short time later, the crest is at:

x = 3 m

The wave pattern has shifted to the right.

Therefore:

Wave direction = right

If we know the time between the snapshots, we can also calculate the wave speed.

---

Worked Example — Wave Speed from Snapshots

A crest moves from:

x = 2.0 m

to:

x = 3.5 m

in:

0.50 s

Distance travelled:

3.5 − 2.0 = 1.5 m

Wave speed:

v = distance / time

v = 1.5 / 0.50

v = 3.0 m/s

Therefore:

Wave speed = 3.0 m/s

---

Representing Longitudinal Waves

Longitudinal waves can also be represented graphically.

A sound wave, for example, consists of alternating:

• Compressions
• Rarefactions

5

Although longitudinal waves do not physically look like a transverse sine curve, quantities such as displacement, pressure, or density can still be plotted against distance or time.

Therefore, a sinusoidal graph does not necessarily mean that the particles physically move up and down.

---

Wave Graphs and Sound

Suppose a microphone records a sound wave.

A graph might show the signal changing with time.

The horizontal axis is therefore:

Time

From this graph, we can determine:

• Period
• Frequency
• Relative amplitude

A higher-frequency sound produces more oscillations in the same time interval.

This type of representation is widely used in:

• Music recording
• Audio editing
• Speech analysis
• Telecommunications

---

Comparing Two Displacement-Time Graphs

Suppose Wave A completes:

2 cycles in 1 second

and Wave B completes:

5 cycles in 1 second

Then:

Wave A frequency = 2 Hz

Wave B frequency = 5 Hz

Wave B has the greater frequency.

Its period is also shorter.

For Wave A:

T = 1/2 = 0.50 s

For Wave B:

T = 1/5 = 0.20 s

Therefore:

Higher frequency → shorter period

---

Worked Example — Counting Cycles

A displacement-time graph shows:

6 complete cycles

during:

3 seconds

Frequency is:

f = number of cycles / time

f = 6 / 3

f = 2 Hz

Period is:

T = 1/f

T = 1/2

T = 0.5 s

Therefore:

Frequency = 2 Hz

Period = 0.5 s

---

Common Mistakes

Mistake: Finding wavelength from a displacement-time graph

A displacement-time graph gives period, not wavelength directly.

Mistake: Finding period from a displacement-distance graph

A displacement-distance graph gives wavelength, not period directly.

Mistake: Ignoring the horizontal axis

Two graphs may look almost identical while representing completely different information.

Always check whether the horizontal axis is:

Distance or time?

Mistake: Measuring wavelength from crest to neighbouring trough

Crest to trough represents half a wavelength.

A complete wavelength can be measured from crest to the next crest.

Mistake: Measuring period from crest to neighbouring trough

Crest to trough represents half a period.

A complete period is measured between equivalent points on consecutive cycles.

Mistake: Measuring amplitude from crest to trough

Amplitude is measured from the equilibrium position to a crest or trough.

Mistake: Assuming the graph shows the physical path of a particle

A wave graph represents displacement. A particle in the medium does not necessarily travel along the shape drawn on the graph.

Mistake: Assuming a displacement-distance graph automatically shows wave direction

A single snapshot generally does not provide enough information to determine the direction of propagation.

---

Key Terms

Displacement – distance and direction from the equilibrium position.

Equilibrium position – the undisturbed position of a point in the medium.

Amplitude – maximum displacement from equilibrium.

Displacement-distance graph – a graph showing displacement against position at one instant.

Displacement-time graph – a graph showing displacement of one point as time passes.

Spatial graph – a representation showing variation with position.

Temporal graph – a representation showing variation with time.

Wavelength – distance between consecutive equivalent points on a wave.

Period – time required for one complete oscillation.

Frequency – number of complete oscillations per second.

Wave profile – the shape of a wave at a particular instant.

---

Check Your Understanding

1. What does a displacement-distance graph represent?

2. What does a displacement-time graph represent?

3. Which type of graph should you use to determine wavelength directly?

4. Which type of graph should you use to determine period directly?

5. Consecutive crests on a displacement-distance graph occur at 3 m and 9 m. Calculate the wavelength.

6. Consecutive crests on a displacement-time graph occur at 1.5 s and 4.0 s. Calculate the period.

7. Calculate the frequency of the wave in Question 6.

8. A graph has a maximum displacement of +4 cm and a minimum displacement of −4 cm. What is the amplitude?

9. Explain why measuring from one crest to the next trough does not give one complete wavelength.

10. A wave has a wavelength of 8 m and a period of 2 s. Calculate its frequency and wave speed.

11. Explain the difference between a spatial wave graph and a temporal wave graph.

12. Sketch a displacement-distance graph for a wave with an amplitude of 2 m and wavelength of 6 m.

13. Sketch a displacement-time graph for an oscillation with an amplitude of 3 cm and period of 4 s.

14. Explain why a single displacement-distance graph usually cannot tell you whether a wave is travelling left or right.

---

Key Takeaways

• Wave graphs allow us to represent displacement, amplitude, wavelength, period, and frequency.
• A displacement-distance graph shows displacement at different positions at one instant.
• A displacement-distance graph is a spatial representation of a wave.
• Wavelength can be determined directly from a displacement-distance graph.
• A displacement-time graph shows how one point changes displacement over time.
• A displacement-time graph is a temporal representation.
• Period can be determined directly from a displacement-time graph.
• Frequency and period are related by f = 1/T.
• The wave equation connects the spatial and temporal descriptions through v = λf.
• During one period, a travelling wave moves forward by one wavelength, so v = λ/T.
• Always inspect the horizontal axis before interpreting a wave graph.
• Amplitude is measured from the equilibrium position to the maximum displacement.
• A single spatial snapshot usually does not reveal the direction in which the wave is travelling.
• Clear wave sketches should include labelled axes, equilibrium position, amplitude, and either wavelength or period, depending on the graph.

 

 

 

5. Wave Energy

Wave Energy

Waves are important because they can transfer energy from one place to another without transferring matter from one place to another overall. Ocean waves can move floating objects, sound waves can make our eardrums vibrate, and electromagnetic waves from the Sun can transfer enormous amounts of energy across space.

The amount of energy carried by a wave depends on several factors, but one of the most important is its amplitude.

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Learning Targets

• I can explain how waves transfer energy.
• I can relate amplitude to energy carried by a wave.
• I can distinguish between energy transfer and material movement.
• I can compare energy carried by different waves.
• I can describe practical applications of wave energy.

Waves Transfer Energy

A wave is a travelling disturbance that transfers energy.

Consider dropping a stone into a pond.

Ripples spread outward from where the stone enters the water.

The disturbance travels across the surface and carries energy away from the point where the stone entered.

If the ripple reaches a floating leaf, the leaf may begin to move.

The moving leaf provides evidence that energy has reached it.

5

The energy has travelled across the water as a wave.

However, this does not mean that the water itself travelled all the way from the stone to the leaf.

Energy Transfer Is Not the Same as Matter Transfer

This is one of the most important ideas in wave physics:

Waves transfer energy without an overall transfer of matter.

Consider a wave travelling along a rope.

If you move one end of the rope up and down, a wave travels along it.

Individual sections of the rope move:

Up and down

but the wave travels:

Along the rope

6

The rope itself does not travel from one end to the other.

Instead, neighbouring sections interact and pass the disturbance — and therefore energy — along the rope.

A Stadium Wave

A stadium wave provides a useful model.

People in the stadium stand up and sit down.

Each person moves only a small distance.

However, the pattern travels around the stadium.

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

Similarly, particles in a medium usually oscillate around their equilibrium positions while the wave disturbance travels through the medium.

Mechanical Waves and Energy

Mechanical waves require a medium through which to travel.

Examples include:

• Sound waves
• Water waves
• Waves on ropes
• Seismic waves
• Waves through springs

The particles of the medium interact with neighbouring particles, allowing energy to move through the material.

6

Without a medium, mechanical waves cannot propagate.

For example, sound cannot travel through a vacuum.

Sound Transfers Energy

When a speaker produces sound, its surface vibrates.

The vibrating speaker causes nearby air particles to oscillate.

These particles interact with neighbouring particles, producing alternating regions of:

• Compression
• Rarefaction

The disturbance travels through the air as a sound wave.

5

When the sound reaches your ear, it transfers energy to your eardrum and causes it to vibrate.

The air molecules themselves do not travel all the way from the speaker to your ear.

Electromagnetic Waves Transfer Energy

Electromagnetic waves can transfer energy without requiring a material medium.

Examples include:

• Radio waves
• Microwaves
• Infrared
• Visible light
• Ultraviolet
• X-rays
• Gamma rays

This means electromagnetic waves can transfer energy through a vacuum.

5

Energy from the Sun travels approximately 150 million kilometres through space before reaching Earth.

Much of this energy is carried by electromagnetic radiation.

Amplitude and Energy

Amplitude is the maximum displacement of a point from its equilibrium position.

A wave with a greater amplitude generally carries more energy than a similar wave with a smaller amplitude.

5

For example, compare two waves travelling along identical ropes.

Wave A has a small amplitude.

Wave B has a much larger amplitude.

The source producing Wave B must move the rope through a greater displacement and do more work on it.

Wave B therefore transfers more energy.

Energy and Amplitude Squared

For many types of waves under the same conditions, the energy transferred is related to the square of the amplitude.

We can represent this approximately as:

Energy ∝ amplitude²

This means the relationship is not simply:

Double amplitude → double energy

Instead:

Double amplitude → about four times the energy

because:

2² = 4

Similarly:

Triple amplitude → about nine times the energy

because:

3² = 9

This relationship applies when comparing otherwise similar waves under conditions where the usual amplitude-squared relationship holds.

Worked Example — Doubling Amplitude

Wave A has amplitude:

2 cm

Wave B has amplitude:

4 cm

Wave B has twice the amplitude of Wave A.

If energy is proportional to amplitude squared:

Energy ratio = 2²

Energy ratio = 4

Therefore:

Wave B carries approximately four times as much energy as Wave A, assuming the other relevant properties are unchanged.

Worked Example — Tripling Amplitude

Suppose one wave has three times the amplitude of another similar wave.

Using:

Energy ∝ amplitude²

we get:

Energy ratio = 3²

Energy ratio = 9

The larger-amplitude wave therefore carries approximately:

9 times as much energy

under the same conditions.

This is why relatively small changes in amplitude can produce large changes in energy transfer.

Amplitude Is Not Wavelength

Amplitude and wavelength describe different properties.

Amplitude measures maximum displacement from equilibrium.

Wavelength measures the distance between corresponding points on consecutive waves.

5

A wave can have:

• Large amplitude and long wavelength
• Large amplitude and short wavelength
• Small amplitude and long wavelength
• Small amplitude and short wavelength

Changing amplitude does not automatically mean wavelength changes.

Energy in Water Waves

Water waves transfer energy across the surface of water.

This can be seen clearly when waves reach a coastline.

Large waves can:

• Move objects
• Erode coastlines
• Damage structures
• Move sediment
• Rock boats

6

The water particles themselves undergo complicated oscillatory motion rather than simply travelling across the ocean with the wave.

The wave energy can nevertheless travel great distances.

Energy in Sound Waves

Sound waves also carry energy.

A quiet sound produces relatively small variations in pressure and particle displacement.

A louder sound generally has a larger amplitude.

Therefore:

Greater sound-wave amplitude → greater intensity

5

This explains why powerful sound waves can physically affect objects.

At sufficiently high intensities, sound can even damage structures or biological tissue.

Energy in Seismic Waves

Earthquakes release large amounts of energy.

Some of this energy travels through Earth as seismic waves.

5

Seismic waves can:

• Shake buildings
• Move the ground
• Damage structures
• Trigger landslides

Scientists also use seismic waves to investigate Earth's internal structure.

Their behaviour provides information about materials deep inside the planet.

Comparing the Energy of Waves

When comparing similar waves, amplitude provides an important indication of the amount of energy being transferred.

Suppose two waves travel through the same medium and have the same frequency.

Wave A has amplitude:

1 cm

Wave B has amplitude:

3 cm

The amplitude ratio is:

3 : 1

If energy is proportional to amplitude squared:

Energy ratio = 3² : 1²

Energy ratio = 9 : 1

Wave B therefore carries approximately nine times as much energy as Wave A under these conditions.

Frequency Can Also Matter

Amplitude is not the only property that can affect the energy carried by a wave.

The relationship between energy and frequency depends on the type of wave and the situation.

For electromagnetic radiation, the energy associated with an individual photon is:

E = hf

where:

• E = photon energy
• h = Planck's constant
• f = frequency

Therefore, higher-frequency electromagnetic radiation has greater energy per photon.

5

This is one reason ultraviolet, X-rays, and gamma rays can have very different effects from radio waves or microwaves.

Energy Can Spread Out

As a wave travels away from its source, its energy may spread over a larger area.

This often causes the wave's intensity to decrease with distance.

Consider sound from a speaker.

Close to the speaker, the sound is relatively intense.

Farther away, the sound becomes weaker.

5

The source has not necessarily started producing less energy.

Instead, the wave's energy is distributed over an increasingly large region.

Absorption

Waves can also lose energy from the wave itself through absorption.

When a material absorbs wave energy, that energy is transferred into other energy stores, often increasing the material's internal energy.

For example:

Sunlight strikes a dark surface.

The surface absorbs some of the electromagnetic radiation.

Its temperature increases.

The energy has not disappeared.

It has been transferred from the electromagnetic wave into the material.

Reflection, Transmission, and Absorption

When a wave reaches a boundary, several things may happen.

Some energy may be:

Reflected

Some may be:

Transmitted

Some may be:

Absorbed

4

The total energy is conserved.

Energy may change form or move into different parts of the system, but it is not created or destroyed.

Practical Application — Solar Energy

Solar panels use energy transferred by electromagnetic waves from the Sun.

Sunlight reaches a photovoltaic cell.

The cell converts some of the incoming electromagnetic energy into electrical energy.

4

The energy pathway can be summarized as:

Sun → electromagnetic waves → solar panel → electrical energy

Not all incoming energy becomes useful electrical energy.

Some is reflected or transferred to thermal energy stores.

Practical Application — Ultrasound

Ultrasound uses high-frequency sound waves.

In medical imaging, ultrasound waves are sent into the body.

Some of the waves are reflected when they encounter boundaries between different tissues.

4

The returning waves are detected and processed to create an image.

Ultrasound therefore uses the transfer and reflection of wave energy to obtain information about structures inside the body.

Practical Application — Sonar

Sonar uses sound waves travelling through water.

A sound pulse is transmitted.

The pulse travels through the water and reflects from an object.

The returning echo is detected.

5

Sonar can be used to:

• Measure water depth
• Locate underwater objects
• Map the ocean floor
• Detect schools of fish

The system relies on sound waves transferring energy through water and returning some of that energy to the detector.

Practical Application — Communication

Electromagnetic waves are essential to modern communication.

Different parts of the electromagnetic spectrum are used for:

• Radio
• Television
• Mobile phones
• Wi-Fi
• Satellite communication
• Fibre-optic communication

5

The waves transfer energy, but they can also be modified to carry information.

Practical Application — Microwave Heating

Microwaves are electromagnetic waves.

In a microwave oven, electromagnetic energy is transferred to food, especially through interactions with polar molecules such as water.

This increases the food's internal energy and temperature.

The energy transfer can be represented as:

Electrical energy → electromagnetic waves → internal energy of food

This is another example of waves being used deliberately to transfer energy.

Practical Application — Wave Power

Ocean waves contain mechanical energy that can potentially be converted into useful electrical energy.

Wave-energy devices can use the movement of water to operate:

• Turbines
• Generators
• Hydraulic systems

6

The energy transfer might be represented as:

Ocean-wave energy → mechanical motion → generator → electrical energy

Wave power is therefore a direct example of humans capturing energy transported by waves.

Practical Application — Earthquake Engineering

Engineers need to understand how seismic waves transfer energy through the ground and into buildings.

When seismic waves reach a structure, they can cause the ground and building to oscillate.

5

Earthquake-resistant buildings may use:

• Flexible structures
• Dampers
• Base isolation
• Reinforced frameworks

These systems help control how seismic energy is transferred through the structure.

Energy Transfer and Conservation of Energy

Waves do not create energy.

The energy carried by a wave must come from somewhere.

For example, when you shake a rope:

Chemical energy in your body

is transferred mechanically to:

The rope

and then travels along the rope as:

Wave energy

Eventually much of this energy may be transferred to the surroundings as thermal energy.

The total amount of energy is conserved.

Worked Example — Comparing Wave Energy

Two otherwise similar waves have amplitudes:

Wave A = 2 mm

Wave B = 6 mm

Find the amplitude ratio:

6 / 2 = 3

Wave B has three times the amplitude.

If:

Energy ∝ amplitude²

then:

Energy ratio = 3²

Energy ratio = 9

Therefore:

Wave B transfers approximately nine times as much energy as Wave A.

Worked Example — Finding an Amplitude Change

Suppose a wave transfers four times as much energy as another otherwise similar wave.

If:

Energy ∝ amplitude²

then:

4 = amplitude ratio²

The amplitude ratio is:

2

Therefore, the higher-energy wave has:

Twice the amplitude

of the original wave.

Wave Energy in Everyday Life

Wave energy transfers occur around us constantly.

When you:

• Hear music, sound waves transfer energy to your ears.
• Feel sunlight, electromagnetic waves transfer energy to your skin.
• Use Wi-Fi, electromagnetic waves travel between devices.
• Speak, your vocal cords create sound waves.
• Watch television, light waves transfer energy to your eyes.
• Use a microwave oven, microwaves transfer energy into food.
• See ripples in water, mechanical waves carry energy across the surface.

Wave physics is therefore not limited to laboratories. It is fundamental to everyday life and modern technology.

Common Mistakes

Mistake: Thinking particles travel with the wave

Particles usually oscillate around equilibrium positions while energy travels through the system.

Mistake: Thinking waves transfer matter

Waves can cause local movement of matter, but there is generally no overall transport of the medium with the wave.

Mistake: Thinking amplitude and energy are the same thing

Amplitude is a measure of displacement.

Energy is the capacity to cause change or do work.

Amplitude provides information about the energy carried by otherwise comparable waves.

Mistake: Assuming twice the amplitude means twice the energy

For many waves under comparable conditions:

Energy ∝ amplitude²

Therefore, doubling amplitude can correspond to approximately four times the energy.

Mistake: Thinking energy disappears when a wave gets weaker

Energy may have:

• Spread over a larger area
• Been absorbed
• Been reflected
• Been transferred into another energy store

Energy is conserved.

Mistake: Thinking electromagnetic waves require matter

Electromagnetic waves can travel through a vacuum.

Mechanical waves require a medium.

Key Terms

Wave energy – energy transferred by a wave.

Amplitude – maximum displacement from equilibrium.

Medium – material through which a mechanical wave travels.

Oscillation – repeated motion around an equilibrium position.

Mechanical wave – a wave that requires a medium.

Electromagnetic wave – a wave that can travel through a vacuum.

Intensity – power transferred per unit area.

Absorption – transfer of wave energy into a material.

Reflection – when a wave returns from a boundary.

Transmission – when a wave passes through a boundary or material.

Seismic wave – a wave carrying energy through Earth.

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

Check Your Understanding

1. What does a wave transfer from one location to another?

2. Explain why a wave can transfer energy without transferring matter overall.

3. Describe what happens to individual sections of a rope when a transverse wave travels along it.

4. How is the amplitude of a wave related to the amount of energy it carries?

5. Two otherwise identical waves have amplitudes of 2 cm and 4 cm. Approximately how many times more energy does the larger-amplitude wave carry?

6. One wave has three times the amplitude of another similar wave. Approximately how many times as much energy does it carry?

7. Explain the difference between amplitude and wavelength.

8. Describe how sound transfers energy from a speaker to your ear.

9. Why can electromagnetic waves transfer energy from the Sun to Earth even though most of the space between them is a vacuum?

10. What can happen to wave energy when a wave reaches a boundary?

11. Explain how ultrasound uses wave energy in medical imaging.

12. Describe one way humans can convert energy carried by waves into useful electrical energy.

Key Takeaways

• Waves transfer energy from one place to another.
• Waves generally do this without an overall transfer of the material through which they travel.
• Particles in a medium usually oscillate around equilibrium positions while the disturbance travels.
• Mechanical waves require a medium.
• Electromagnetic waves can transfer energy through a vacuum.
• Greater amplitude generally means greater energy transfer for otherwise similar waves.
• For many waves, energy is approximately proportional to amplitude squared.
• Doubling amplitude can therefore correspond to approximately four times the energy.
• Wave energy may be reflected, transmitted, absorbed, or spread over a larger area.
• Energy transferred by waves obeys the principle of conservation of energy.
• Sound, ultrasound, seismic waves, sunlight, communications, sonar, and ocean-wave power all demonstrate practical uses or effects of wave energy.
• Understanding wave energy is important in medicine, communications, renewable energy, engineering, astronomy, and everyday life.

Did You Know?

A large ocean swell can travel thousands of kilometres across an ocean while individual water particles remain relatively close to their original locations. What travels across the ocean is primarily the wave disturbance and its energy, not the same body of water moving all the way from one coastline to another.