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.

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.

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.

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.

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.

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.

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.

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.

Comparing Frequency and Period

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.