Physics

5.1 - Longitudinal & Transverse Waves

8 min

Energy and wave features

Period and frequency

The wave speed equation

Transverse and longitudinal waves

note 1 of 5

Waves transfer energy, not matter

A wave transfers energy without transferring matter.
As a wave travels through a medium, the particles vibrate and pass energy from one to the next, but overall the particles stay in the same place.

A row of blue vertical lines bunched together in some places and spread out in others, with a small double arrow labelled particle movement and an orange arrow labelled direction of energy transfer.

Examples

Ripples spreading across a pool don't carry the water (or a floating twig) away.
Sound waves reach a listener's ear without carrying the air away from the source.
Waves can also carry information, such as light along an optical fibre or radio waves through the air.

note 2 of 5

Amplitude, wavelength, frequency and period

Amplitude - The maximum displacement of a point on the wave from its undisturbed (rest) position.
Wavelength ( $λ$ ) - The distance between the same point on two adjacent waves, such as crest to crest or trough to trough.
Frequency ( $f$ ) - The number of complete waves passing a fixed point each second.
Period ( $T$ ) - The time taken for one complete wave to pass a fixed point.

Reading properties from graphs

A graph of displacement against distance shows wavelength and amplitude.
A graph of displacement against time shows period and amplitude.

A wave on a displacement axis in metres with a crest and a trough labelled, the amplitude marked from the rest line up to a crest, and the wavelength marked from one trough to the next.

Wavefronts

A wavefront is an imaginary line or surface joining points on adjacent waves that are at the same point in their cycle (e.g. along a crest).
The distance between one wavefront and the next equals one wavelength.

Two blue wave curves travelling to the right, cut by three tilted orange rectangles labelled wavefront, with the curves labelled wave and a grey arrow labelled direction of travel.

note 3 of 5

Transverse and longitudinal waves

Waves are classified by the direction the particles vibrate compared with the direction energy is transferred.

Transverse waves

Vibrations are perpendicular (at 90°) to the direction of energy transfer.
Examples:
- All electromagnetic waves (e.g. light)
- Ripples on water
- Seismic S-waves
- Waves on a string

A grey slinky spring shaped into a wave, beside a blue arrow labelled wave travelling this way crossed by two pink double arrows labelled vibrations from side to side.

Longitudinal waves

Vibrations are parallel to the direction of energy transfer.
Longitudinal waves show areas of:
- Compression - Where particles are squashed together
- Rarefaction - Where particles are spread apart
Examples:
- Sound waves and ultrasound
- Seismic P-waves

Particles spread along a line under an arrow labelled direction of energy transfer, with a sparse region boxed and labelled rarefaction and a crowded region boxed and labelled compression.

note 4 of 5

The wave speed equation

Wave speed is the speed at which energy is transferred through a medium.
The wave equation applies to all waves.

Formula for wave speed

$v = f λ$

Where:

$v$ = Wave speed, in metres per second (m/s)
$f$ = Frequency, in hertz (Hz)
$λ$ = Wavelength, in metres (m)

A formula triangle with v in the top section and f multiplied by lambda below, labelled wave speed (m/s), frequency (Hz) and wavelength (m). — Cover the quantity you want to find to rearrange the equation.

note 5 of 5

Worked example - Wavelength from frequency

A radio wave has a frequency of 7.5 × 10⁶ Hz. The speed of radio waves in air is 3.0 × 10⁸ m/s. Find its wavelength.

Step 1 - Formula

$v = f λ$

Step 2 - Rearrange the formula

$λ = \frac{v}{f}$

Step 3 - Substitution and calculation

$λ = \frac{3.0 \times 10^{8}}{7.5 \times 10^{6}} = 40 m$

The wavelength of the radio wave is 40 m.

key terms

TermDefinition

AmplitudeThe maximum displacement of a point on a wave from its undisturbed position.

WavelengthThe distance between the same point on two adjacent waves.

FrequencyThe number of times something happens each second. For a wave, it is the number of complete waves passing a point each second, measured in hertz (Hz).

PeriodThe time taken for one complete cycle of something that repeats, such as one complete wave passing a point, one swing of a pendulum or one orbit.

Transverse waveA wave where the vibrations are perpendicular to the direction of energy transfer.

Longitudinal waveA wave where the vibrations are parallel to the direction of energy transfer.

CompressionA region in a longitudinal wave where the particles are squashed close together.

RarefactionA region in a longitudinal wave where the particles are spread further apart.

end of notes

Key points to remember

Amplitude, wavelength, frequency and period

Amplitude - The maximum displacement of a point on the wave from its undisturbed (rest) position.

Wavelength ( $λ$ ) - The distance between the same point on two adjacent waves, such as crest to crest or trough to trough.

Frequency ( $f$ ) - The number of complete waves passing a fixed point each second.

Period ( $T$ ) - The time taken for one complete wave to pass a fixed point.

Reading properties from graphs

A graph of displacement against distance shows wavelength and amplitude.

A graph of displacement against time shows period and amplitude.

Transverse and longitudinal waves

Waves are classified by the direction the particles vibrate compared with the direction energy is transferred.

Transverse waves

Vibrations are perpendicular (at 90°) to the direction of energy transfer.

Examples:

All electromagnetic waves (e.g. light)
Ripples on water
Seismic S-waves
Waves on a string