A sound wave travels through air. The wave has a period of 0.002 s and a speed of 340 m/s. Using your knowledge of wave features, explain how the frequency and wavelength of this wave are related to these values, and describe what would happen to the wavelength if the frequency were doubled while the wave speed remained constant.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Sound waves are longitudinal waves that transfer energy through a medium. Like all waves, they can be described using features such as frequency, period, wavelength, amplitude, and wave speed.
Model answer (4 marks)
Frequency is the number of complete cycles that pass a point each second. It is the reciprocal of the period, so
f = 1/T = 1/0.002 s = 500 Hz.
Wavelength is the distance between two successive points that are in phase – the length of one complete wave cycle.
Wave speed is the product of frequency and wavelength:
v = f × λ.
With v = 340 m s⁻¹ and f = 500 Hz, λ = v/f = 340/500 = 0.68 m.
If the frequency were doubled to 1000 Hz while the speed stayed 340 m s⁻¹, the wavelength would be halved:
λ' = v/f' = 340/1000 = 0.34 m.
Thus the wavelength is inversely proportional to frequency when the speed is constant.
f = 1/T = 1/0.002 s = 500 Hz.
Wavelength is the distance between two successive points that are in phase – the length of one complete wave cycle.
Wave speed is the product of frequency and wavelength:
v = f × λ.
With v = 340 m s⁻¹ and f = 500 Hz, λ = v/f = 340/500 = 0.68 m.
If the frequency were doubled to 1000 Hz while the speed stayed 340 m s⁻¹, the wavelength would be halved:
λ' = v/f' = 340/1000 = 0.34 m.
Thus the wavelength is inversely proportional to frequency when the speed is constant.
Examiner tips
- Show the calculation for f = 1/T and λ = v/f to gain full marks.
- Explain the inverse relationship clearly – frequency up, wavelength down.
- Mention the numerical example to demonstrate understanding.
Common mistakes
- Using λ = v × f instead of λ = v/f.
- Forgetting to convert period to frequency before calculating wavelength.
- Not recognising that doubling f halves λ when v is constant.
Mark scheme (4 marks)
- Frequency is the number of complete waves (cycles) passing a point per second / frequency is the reciprocal of the period
- Wavelength is the distance between two successive points in phase / distance of one complete wave cycle
- Wave speed = frequency × wavelength, so frequency and wavelength are inversely proportional when wave speed is constant
- If frequency is doubled and wave speed stays the same, the wavelength is halved
Key terms in this question
frequency · wavelength · wave speed · period
Related
- All WJEC GCSE Physics (Wales) revision notes →
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- Decode the mark scheme abbreviations →
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