# 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.

> IB DP Physics Higher Level (2023 syllabus) — C.4 Standing waves and resonance · Explain · 4 marks

## Mark scheme (4 marks)

1. The wave speed on a stretched string increases when tension increases
2. 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
3. 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
4. Quantitative reasoning: wave speed v = √(T/μ), so v ∝ √T, meaning the fundamental frequency f ∝ √T and increases with tension

## Key terms

- [fundamental frequency](https://www.gradenine.co.uk/glossary/fundamental-frequency)
- [standing wave](https://www.gradenine.co.uk/glossary/standing-wave)
- [tension](https://www.gradenine.co.uk/glossary/tension)

## Related

- [Revision notes for IB DP Physics Higher Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
- [Practice this with AI marking (free)](https://www.gradenine.co.uk/start)

---
Source: [GradeNine](https://www.gradenine.co.uk/q/explain-why-the-fundamental-frequency-of-6ac555b6) · Published by Druglandscape Ltd.