# Explain why an open pipe and a closed pipe of the same length produce different fundamental frequencies.

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

> A musician notices that a cylindrical pipe closed at one end sounds a lower fundamental note than an otherwise identical pipe open at both ends.

## Mark scheme (4 marks)

1. In an open pipe, displacement antinodes must form at both open ends, so the fundamental mode fits exactly half a wavelength in the pipe length L, giving λ = 2L.
2. In a closed pipe, a displacement node forms at the closed end and an antinode at the open end, so the fundamental mode fits only a quarter wavelength in the same length L, giving λ = 4L.
3. Since frequency f = v/λ and the wave speed v is the same in both pipes, the closed pipe has a longer fundamental wavelength (4L > 2L) and therefore a lower fundamental frequency.
4. The fundamental frequency of the closed pipe is half that of the open pipe of the same length (f_closed = f_open / 2), so the closed pipe sounds a lower note.

## Key terms

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

## 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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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-why-an-open-pipe-and-c653b2ba) · Published by Druglandscape Ltd.