A student says: 'A wave with a higher frequency must have a longer wavelength.' Explain why this statement is incorrect, and describe how frequency and wavelength are actually related when the wave speed stays the same.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Sound waves travel at approximately 340 m/s through air. A low-pitched sound has a frequency of 85 Hz, while a high-pitched sound has a frequency of 340 Hz.
Model answer (4 marks)
A higher frequency does not give a longer wavelength – it gives a shorter one when the speed is unchanged.
Wave speed v = f × λ. If v is constant, λ = v/f, so λ is inversely proportional to f.
For the two sounds, 85 Hz has a longer wavelength than 340 Hz because λ₁/λ₂ = f₂/f₁ = 340/85 = 4.
Thus the student’s statement is wrong: at constant speed a higher frequency means a shorter wavelength.
Wave speed v = f × λ. If v is constant, λ = v/f, so λ is inversely proportional to f.
For the two sounds, 85 Hz has a longer wavelength than 340 Hz because λ₁/λ₂ = f₂/f₁ = 340/85 = 4.
Thus the student’s statement is wrong: at constant speed a higher frequency means a shorter wavelength.
Examiner tips
- Show the formula v = fλ and explain the inverse relationship when v is constant.
- Give the comparative statement for the two sounds – 85 Hz has a longer λ than 340 Hz.
- Use the word ‘shorter’ to describe the higher‑frequency wave.
- Mention that the speed is constant (340 m/s).
Common mistakes
- Confusing ‘higher frequency gives longer wavelength’ with ‘higher frequency gives shorter wavelength’.
- Forgetting to state that the speed is constant.
- Not using the correct units or the formula v = fλ.
Mark scheme (4 marks)
- Wave speed equals frequency multiplied by wavelength (wave speed = frequency × wavelength)
- When wave speed is constant, frequency and wavelength are inversely proportional / as one increases the other decreases
- The low-pitched sound (85 Hz) has a longer wavelength than the high-pitched sound (340 Hz) / correct comparative statement about the two sounds given
- Therefore the student's statement is wrong because a higher frequency gives a shorter, not longer, wavelength (at constant wave speed)
Key terms in this question
frequency · wavelength · wave speed
Related
- All WJEC GCSE Physics (Wales) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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