# Explain how resonance occurs in a tube open at both ends when a sound source is placed near one end, and explain why only certain frequencies cause resonance in such a tube.

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

> A loudspeaker producing a continuous sinusoidal tone of variable frequency is placed near one open end of a tube that is open at both ends. As the frequency is slowly increased from a low value, resonance is observed at several distinct frequencies.

## Mark scheme (4 marks)

1. The sound wave from the loudspeaker travels along the tube and reflects at the far open end, producing a wave travelling in the opposite direction.
2. The incident and reflected waves superpose (interfere) to form a standing wave inside the tube.
3. A displacement antinode must be present at each open end, so resonance occurs only when the tube length is a whole number of half-wavelengths (L = nλ/2, where n = 1, 2, 3, …).
4. Resonance occurs because at these specific frequencies the standing wave is sustained with maximum amplitude, as energy is continuously transferred from the source to the oscillating air column at the natural frequency of the tube.

## Key terms

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

## 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)
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