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How do we describe and measure a wave?

Properties of waves: amplitude, wavelength, frequency and period, the wave speed equation, and the required practical for measuring wave speed.

A focused answer to AQA GCSE Physics 4.6.1, covering the amplitude, wavelength, frequency and period of a wave, the wave speed equation, the period equation, and the required practical for measuring the speed of waves.

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  1. What this dot point is asking
  2. Describing a wave
  3. Frequency and period
  4. The wave speed equation
  5. Required practical: measuring wave speed
  6. Try this

What this dot point is asking

AQA wants you to define amplitude, wavelength, frequency and period, use the wave speed and period equations, and describe the required practical for measuring the speed of waves. This is part of topic 4.6.1 of the AQA GCSE Physics (8463) specification, and the measurement of wave speed is a named required practical.

Describing a wave

Frequency and period

The period and frequency describe the same thing from opposite viewpoints: frequency counts how many waves pass each second, while period times how long one wave takes. A wave with a frequency of 50 Hz50\,Hz has a period of 1/50=0.02 s1/50 = 0.02\,s. Because they are reciprocals, doubling the frequency halves the period. Both quantities are set by the source of the wave (how fast it vibrates) and do not change when the wave moves into a new material, even though the speed and wavelength can change.

The wave speed equation

This single equation links the three key wave quantities, so given any two you can find the third. It applies to every kind of wave, from sound and water waves to the whole electromagnetic spectrum. A subtle point AQA tests is what happens when a wave crosses into a new medium: the frequency is fixed by the source and stays the same, so if the speed changes (as light does on entering glass) then the wavelength must change to keep the equation balanced. Watch the units carefully and always convert kilohertz or megahertz to hertz, and centimetres to metres, before substituting.

Required practical: measuring wave speed

For water waves, use a ripple tank: measure the frequency from the vibrating dipper and the wavelength by viewing the shadow pattern, then use v=fλv = f\lambda. For waves on a string, set up standing waves with a signal generator and vibration transducer, measure the wavelength and read the frequency, then apply v=fλv = f\lambda.

Accuracy in these practicals depends on measuring the wavelength over several waves and dividing, rather than trying to measure a single wavelength, because a small error on one wavelength is reduced when spread over many. In the ripple tank, using a strobe or freezing the shadow image makes the moving wavefronts easier to measure. On the string, you adjust the frequency until a clear standing-wave pattern forms, then measure across several loops to find the wavelength. These methods let you confirm the wave equation experimentally for both a transverse water wave and a transverse wave on a string. The amplitude of a wave, separately, is linked to how much energy it carries: a wave with a larger amplitude transfers more energy, which for sound means a louder sound and for light a brighter beam.

Try this

Q1. Define the wavelength of a wave. [1 mark]

  • Cue. The distance between the same point on two adjacent waves.

Q2. A wave has a frequency of 20 Hz20\,Hz and a wavelength of 1.5 m1.5\,m. Calculate its speed. [2 marks]

  • Cue. v=fλ=20×1.5=30 m/sv = f\lambda = 20 \times 1.5 = 30\,m/s.

Exam-style practice questions

Practice questions written in the style of AQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

AQA 20195 marksA radio station broadcasts at a frequency of 200 kHz200\,\text{kHz}. Radio waves travel at 3.0×108 m/s3.0 \times 10^{8}\,\text{m/s}. Calculate the wavelength of the radio waves, and calculate the period of the wave.
Show worked answer →

First convert the frequency to hertz: 200 kHz=200,000 Hz200\,\text{kHz} = 200{,}000\,\text{Hz}, which is 2.0×105 Hz2.0 \times 10^{5}\,\text{Hz} (1 mark, a common slip). Use v=fλv = f\lambda rearranged to λ=v/f=3.0×1082.0×105=1500 m\lambda = v / f = \frac{3.0 \times 10^{8}}{2.0 \times 10^{5}} = 1500\,\text{m} (2 marks). The period is T=1/f=12.0×105=5.0×10−6 sT = 1 / f = \frac{1}{2.0 \times 10^{5}} = 5.0 \times 10^{-6}\,\text{s} (2 marks). Markers reward the conversion of kHz to Hz, rearranging the wave equation for wavelength, and using T=1/fT = 1/f for the period. The most frequent error is leaving the frequency in kHz.

AQA 20213 marksDefine the amplitude and the wavelength of a wave, and explain why the amplitude and the frequency of a wave are independent of each other.
Show worked answer →

The amplitude is the maximum displacement of a point on the wave from its rest (undisturbed) position (1 mark). The wavelength is the distance between the same point on two adjacent waves, for example from one crest to the next (1 mark). The amplitude and frequency are independent because amplitude describes how far the wave oscillates (related to the energy carried), while frequency describes how many waves pass each second (related to how quickly the source vibrates); you can change one without changing the other, for example a louder sound has a greater amplitude but the same frequency (pitch) (1 mark). Markers reward the two definitions and a clear statement that amplitude and frequency describe different, unconnected features of the wave.

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