# Explain why a string fixed at both ends can only sustain standing waves at specific frequencies.

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

> A string of length L is fixed at both ends and is set into vibration. Only certain frequencies produce sustained, stable patterns of vibration on the string.

## 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 must be nodes (zero displacement) because the string cannot move at a fixed boundary.
3. Only wavelengths for which a whole number of half-wavelengths fit exactly between the two fixed ends satisfy the boundary conditions.
4. Since frequency and wavelength are related by f = v/λ, only discrete (quantised) frequencies corresponding to the allowed wavelengths are possible, forming the harmonic series.

## Key terms

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

## 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)

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