Wave Properties — Amplitude, Frequency, Wavelength and Period

This lesson covers the four key properties used to describe any wave — amplitude, frequency, wavelength and period — as required by AQA GCSE Combined Science Trilogy (8464), Physics Paper 2, section 6.1. You must be able to define each property, identify it on a wave diagram, and use the relationship between frequency and period.

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The Four Key Wave Properties

Property	Symbol	Unit	Definition
Amplitude	A	metres (m)	Maximum displacement of a point on the wave from its undisturbed (equilibrium) position
Wavelength	λ (lambda)	metres (m)	Distance between two consecutive points in phase (e.g. crest to crest or compression to compression)
Frequency	f	hertz (Hz)	Number of complete waves passing a point per second
Period	T	seconds (s)	Time taken for one complete wave to pass a point

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Amplitude

The amplitude is the maximum displacement from the rest (equilibrium) position.

• For a transverse wave: measured from the rest position to the crest (or the rest position to the trough).
• It is not the distance from crest to trough — that is twice the amplitude.
• A larger amplitude means the wave carries more energy.

Amplitude and Energy

Amplitude	Energy carried	Sound equivalent	Light equivalent
Large	More energy	Louder sound	Brighter light
Small	Less energy	Quieter sound	Dimmer light

Exam Tip: A very common mistake is measuring amplitude from crest to trough. Always measure from the rest position to the crest (or rest position to the trough). This is often tested on diagram-reading questions.

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Wavelength

The wavelength (λ) is the distance between one point on a wave and the equivalent point on the next wave.

• For a transverse wave: crest to crest, or trough to trough.
• For a longitudinal wave: compression to compression, or rarefaction to rarefaction.

graph LR
    subgraph "Measuring Wavelength"
    direction LR
    A["Crest 1"] -->|"λ (wavelength)"| B["Crest 2"]
    B -->|"λ"| C["Crest 3"]
    end

Exam Tip: On a displacement–distance graph, wavelength is the horizontal distance between two successive crests (or two successive troughs). On a displacement–time graph, the horizontal distance gives you the period, not the wavelength.

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Frequency

The frequency (f) is the number of complete waves passing a point every second.

• Unit: hertz (Hz). 1 Hz = 1 wave per second.
• A higher frequency means more waves pass each second.
• For sound: higher frequency = higher pitch.
• Frequency does not change when a wave moves from one medium to another.

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Period

The period (T) is the time for one complete wave to pass a given point.

• Unit: seconds (s).
• A shorter period means a higher frequency.

The Frequency–Period Relationship

$f = \frac{1}{T}$f=T1​

$T = \frac{1}{f}$T=f1​

where:

• $f$f = frequency in hertz (Hz)
• $T$T = period in seconds (s)

Worked Example 1

A wave has a period of 0.04 s. Calculate its frequency.

$f = \frac{1}{T} = \frac{1}{0.04} = 25 \text{ Hz}$f=T1​=0.041​=25 Hz

Worked Example 2

A radio station broadcasts at a frequency of 100 000 Hz. What is the period of the wave?

$T = \frac{1}{f} = \frac{1}{100\,000} = 1 \times 10^{-5} \text{ s} = 0.00001 \text{ s}$T=f1​=1000001​=1×10−5 s=0.00001 s

Exam Tip (AQA 8464): Make sure you can rearrange $f = 1/T$f=1/T for both $f$f and $T$T. These quick calculations often appear as 1-mark questions. Always include units in your answer.

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Reading a Wave Diagram

Displacement–Distance Graph

A displacement–distance graph is a snapshot of the wave at one instant in time.

• The x-axis shows distance (m).
• The y-axis shows displacement (m).
• Wavelength = horizontal distance between two consecutive crests (or troughs).
• Amplitude = maximum vertical displacement from the rest position (the x-axis).

Displacement–Time Graph

A displacement–time graph shows how the displacement of one point changes over time.

• The x-axis shows time (s).
• The y-axis shows displacement (m).
• Period = horizontal distance between two consecutive crests.
• Amplitude = maximum vertical displacement from the rest position.

Graph type	x-axis	Horizontal measurement gives
Displacement–distance	Distance (m)	Wavelength (λ)
Displacement–time	Time (s)	Period (T)

Exam Tip: Students frequently confuse wavelength and period on graphs. Remember: wavelength comes from a distance graph; period comes from a time graph. This distinction is tested regularly at GCSE.

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Common Mistakes

Mistake	Correction
Measuring amplitude from crest to trough	Amplitude is from the rest position to the crest — half the crest-to-trough distance
Reading wavelength from a time graph	A time graph gives you the period, not the wavelength
Forgetting units on frequency	Frequency is always in hertz (Hz)
Saying frequency changes when a wave enters a new medium	Frequency stays the same — only speed and wavelength change

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Summary

• Amplitude = maximum displacement from the rest position (measured in metres).
• Wavelength (λ) = distance between two consecutive equivalent points (crest to crest or compression to compression).
• Frequency (f) = number of complete waves per second, measured in hertz (Hz).
• Period (T) = time for one complete wave, measured in seconds.
• $f = 1/T$f=1/T and $T = 1/f$T=1/f.
• A displacement–distance graph shows wavelength; a displacement–time graph shows period.
• Larger amplitude means more energy transferred by the wave.

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Deeper Worked Examples

AQA examiners mix up displacement–distance and displacement–time graphs, and they test the relationship T = 1/f repeatedly. These four worked examples cover the main patterns you will meet in Paper 2.

Worked Example 1 — Period and frequency

A pendulum completes 20 swings in 40 seconds. Calculate the period and frequency.

• Period: T = total time ÷ number of swings = 40 ÷ 20 = 2.0 s.
• Frequency: f = 1 / T = 1 / 2.0 = 0.5 Hz.