Explain why the fundamental frequency of a standing wave on a stretched string increases when the tension in the string is increased, whilst the length of the string remains constant.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (4 marks)
The wave speed on a stretched string is v=√(T/μ). When the tension T is increased, v increases.
For a string fixed at both ends the fundamental mode must have nodes at the ends, so its wavelength is λ=2L, which is fixed because L is constant.
Frequency is f=v/λ. With λ unchanged, the increase in v gives a proportional increase in f.
Thus f∝√T, so the fundamental frequency rises when the tension is increased.
For a string fixed at both ends the fundamental mode must have nodes at the ends, so its wavelength is λ=2L, which is fixed because L is constant.
Frequency is f=v/λ. With λ unchanged, the increase in v gives a proportional increase in f.
Thus f∝√T, so the fundamental frequency rises when the tension is increased.
Examiner tips
- Show the wave‑speed equation and explain the dependence on tension.
- State that λ=2L for the fundamental and that L is constant.
- Use f=v/λ to link the increase in v to an increase in f.
- Mention the proportionality f∝√T for clarity.
Common mistakes
- Confusing the fundamental wavelength with higher harmonics.
- Forgetting that λ remains 2L when tension changes.
- Using the wrong wave‑speed formula (e.g. v=√(T/ρ) instead of μ).
Mark scheme (4 marks)
- The wave speed on a stretched string increases when tension increases
- For a string fixed at both ends, the boundary conditions require nodes at each end, fixing the wavelength of the fundamental mode at twice the string length
- Since frequency equals wave speed divided by wavelength (f = v/λ), and wavelength is unchanged, the increase in wave speed produces a proportional increase in frequency
- Quantitative reasoning: wave speed v = √(T/μ), so v ∝ √T, meaning the fundamental frequency f ∝ √T and increases with tension
Key terms in this question
fundamental frequency · standing wave · tension
Related
- All IB DP Physics Higher Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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