# Explain why a stretched string fixed at both ends can only vibrate at certain discrete frequencies.

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

> A musician plucks a stretched string that is fixed at both ends. The string is observed to vibrate in several different patterns, each at a specific frequency.

## Mark scheme (4 marks)

1. A standing wave is formed by the superposition (interference) of two waves travelling in opposite directions along the string.
2. The fixed ends of the string must be nodes (zero displacement), so only whole numbers of half-wavelengths fit between the two fixed ends.
3. This boundary condition restricts the allowed wavelengths to a discrete set (λ = 2L/n), so only specific wavelengths can form stable standing waves.
4. Since wave speed on the string is fixed (for given tension and mass per unit length), each allowed wavelength corresponds to a unique frequency (f = v/λ), giving a discrete set of resonant frequencies.

## Related

- [Revision notes for IB DP Physics Standard 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-a-stretched-string-fixed-68512dc7) · Published by Druglandscape Ltd.