# Explain how resonance occurs in a closed pipe and why the pipe supports only odd harmonics.

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

> A closed pipe is one that is sealed at one end and open at the other. When a sound source is placed near the open end, the pipe can resonate at certain frequencies.

## Mark scheme (4 marks)

1. A displacement node (pressure antinode) must form at the closed end and a displacement antinode (pressure node) must form at the open end.
2. When the frequency of the source matches a natural frequency of the pipe, the incident and reflected waves superpose to form a standing wave, producing resonance.
3. The shortest resonating length contains one quarter-wavelength (λ/4), so the fundamental has a wavelength four times the pipe length.
4. Only odd multiples of the fundamental frequency (1st, 3rd, 5th harmonics…) satisfy the node-at-closed-end and antinode-at-open-end boundary conditions simultaneously, so even harmonics cannot form.

## Key terms

- [resonance](https://www.gradenine.co.uk/glossary/resonance)
- [harmonics](https://www.gradenine.co.uk/glossary/harmonics)
- [closed pipe](https://www.gradenine.co.uk/glossary/closed-pipe)

## 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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