Wave Properties

This lesson covers the key properties of waves — including wavelength, frequency, amplitude, period and wave speed — as required by the AQA GCSE Physics specification (4.6.1). You will learn the definitions of each property, the equations that link them, and how to read values from wave diagrams and graphs.

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Key Wave Properties

Every wave can be described using the following properties:

Property	Symbol	Unit	Definition
Wavelength	lambda	metres (m)	The distance from one point on a wave to the same point on the next wave
Frequency	f	hertz (Hz)	The number of waves passing a point per second
Amplitude	A	metres (m)	The maximum displacement of a point from its rest (equilibrium) position
Period	T	seconds (s)	The time taken for one complete wave to pass a point
Wave speed	v	metres per second (m/s)	The speed at which the wave travels through the medium

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Wavelength

The wavelength is the distance between one point on a wave and the same point on the next wave. It is measured in metres (m).

For a transverse wave, wavelength can be measured:

• From peak to peak (crest to crest).
• From trough to trough.
• From any point to the next identical point.

For a longitudinal wave, wavelength is measured:

• From the centre of one compression to the centre of the next compression.
• From the centre of one rarefaction to the centre of the next rarefaction.

Exam Tip: When measuring wavelength on a diagram, always measure between two identical points — peak to peak or trough to trough. Do NOT measure from peak to trough, as this is only half a wavelength. This is one of the most common mistakes in the exam.

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Frequency

The frequency of a wave is the number of complete waves (cycles) passing a fixed point per second. It is measured in hertz (Hz).

• 1 Hz = 1 wave per second.
• 1 kHz (kilohertz) = 1 000 Hz.
• 1 MHz (megahertz) = 1 000 000 Hz.

If 50 waves pass a point in 10 seconds, the frequency is:

f = number of waves / time = 50 / 10 = 5 Hz

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Amplitude

The amplitude is the maximum displacement of a point on the wave from its rest position (the undisturbed position, also called the equilibrium position).

• Amplitude is measured from the rest position to the peak (or from the rest position to the trough).
• Amplitude is NOT measured from peak to trough — that distance is twice the amplitude.
• A larger amplitude means the wave carries more energy.

Exam Tip: The amplitude is measured from the middle (rest position) to the top (peak), NOT from the bottom to the top. If a question gives you the total height from trough to peak, you must halve it to find the amplitude.

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Period

The period (T) of a wave is the time taken for one complete wave (one full cycle) to pass a fixed point. It is measured in seconds (s).

The period and frequency are related by the equation:

T = 1 / f

And rearranged:

f = 1 / T

Frequency (Hz)	Period (s)
1	1.0
2	0.5
5	0.2
10	0.1
50	0.02
100	0.01
1 000	0.001

Worked Example

A wave has a frequency of 250 Hz. Calculate its period.

T = 1 / f = 1 / 250 = 0.004 s

Exam Tip: This equation is on the AQA equation sheet, but you should know it by heart. Remember: a high frequency means a short period, and a low frequency means a long period. They are inversely proportional.

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The Wave Equation

The wave equation links wave speed, frequency and wavelength:

v = f x lambda

Where:

• v = wave speed (m/s)
• f = frequency (Hz)
• lambda = wavelength (m)

This equation applies to all types of waves — transverse, longitudinal, mechanical and electromagnetic.

Rearranging the Wave Equation

To find	Rearrangement
Wave speed	v = f x lambda
Frequency	f = v / lambda
Wavelength	lambda = v / f

Worked Example 1

A sound wave has a frequency of 440 Hz and a wavelength of 0.77 m. Calculate the wave speed.

v = f x lambda = 440 x 0.77 = 338.8 m/s

Worked Example 2

A radio wave travels at 3 x 10^8 m/s and has a wavelength of 1 500 m. Calculate its frequency.

f = v / lambda = (3 x 10^8) / 1 500 = 200 000 Hz = 200 kHz

Worked Example 3

A water wave has a speed of 2.4 m/s and a frequency of 0.8 Hz. Calculate the wavelength.

lambda = v / f = 2.4 / 0.8 = 3.0 m

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Reading Wave Diagrams

A displacement-distance graph shows the shape of a wave at a single moment in time.

graph LR
    subgraph "Displacement-Distance Graph"
        A["Wavelength: peak to peak"]
        B["Amplitude: rest to peak"]
    end

From a displacement-distance graph you can read:

• Wavelength — the horizontal distance from one peak to the next peak (or trough to trough).
• Amplitude — the vertical distance from the rest position (x-axis) to the peak.

A displacement-time graph shows how the displacement of a single point on the wave changes over time.

From a displacement-time graph you can read:

• Period — the horizontal distance for one complete cycle (peak to peak on the time axis).
• Amplitude — the vertical distance from the rest position to the peak.
• Frequency — calculated using f = 1 / T.

Graph Type	x-axis	You can find
Displacement-distance	Distance (m)	Wavelength, amplitude
Displacement-time	Time (s)	Period, amplitude, frequency