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

4. Representing Waves

5. Wave Energy