# Explain how a standing wave is formed on a stretched string that is fixed at both ends, and outline the conditions that determine which harmonics can be sustained.

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

> A guitar string is plucked so that it vibrates transversely. The string has a fixed length L and is attached firmly at both ends.

## Mark scheme (4 marks)

1. Two waves of the same frequency (and amplitude) travel in opposite directions along the string and superpose.
2. The fixed ends must be nodes because the string cannot displace at a fixed point, so the reflected wave undergoes a phase change of π (half a wavelength).
3. A whole number of half-wavelengths must fit exactly into the length L, i.e. L = nλ/2, where n is a positive integer.
4. Because both ends are nodes, all harmonics (n = 1, 2, 3, …) are permitted, so the string supports a fundamental frequency and all integer multiples of it.

## Key terms

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

## 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)

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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-how-a-standing-wave-is-ea3f27c7) · Published by Druglandscape Ltd.