# Explain how the principle of superposition accounts for the formation of a standing wave when two identical waves travel in opposite directions along the same medium.

> IB DP Physics Standard Level (2023 syllabus) — C.2 Wave model · Explain · 4 marks

> Two identical travelling waves of the same frequency, amplitude, and wavelength move in opposite directions along a stretched string.

## Mark scheme (4 marks)

1. The principle of superposition states that when two waves meet, the resultant displacement at any point is the vector (algebraic) sum of the individual displacements.
2. At certain points (nodes), the two waves are always in antiphase, so their displacements cancel to give zero resultant displacement at all times.
3. At antinodes, the two waves are always in phase, so their displacements add constructively, producing maximum amplitude (equal to twice the amplitude of each wave).
4. The pattern of nodes and antinodes does not travel along the medium — energy is stored in the pattern rather than transported, which is why the superposition of the two oppositely travelling waves produces a standing (stationary) wave.

## Key terms

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

## 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)
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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-how-the-principle-of-superposition-a0d3b3f6) · Published by Druglandscape Ltd.