# Explain how the superposition of two waves produces a standing wave, and state the conditions on the two waves that are necessary for this to occur.

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

> Two waves travel in opposite directions along a stretched string. At certain frequencies, a stable pattern is observed in which some points on the string remain stationary while others vibrate with maximum amplitude.

## Mark scheme (4 marks)

1. The two waves overlap/superpose and the resultant displacement at each point is the vector sum of the individual displacements.
2. The two waves must have the same frequency (and wavelength) and the same (or very similar) amplitude.
3. The two waves must travel in opposite directions.
4. At nodes the two waves are always in antiphase (phase difference of π / 180°), so they destructively interfere and the displacement is permanently zero; at antinodes they are always in phase, giving maximum constructive interference and maximum amplitude.

## Key terms

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

## 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-the-superposition-of-two-278752c1) · Published by Druglandscape Ltd.