Explain why an open pipe and a closed pipe of the same length produce different fundamental frequencies.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
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.
Model answer (4 marks)
In an open pipe both ends are open, so displacement antinodes must occur at the two ends. The lowest‑order standing wave that satisfies this has half a wavelength inside the pipe, so λ=2L. In a pipe closed at one end the closed end must be a displacement node and the open end an antinode. The lowest‑order standing wave then contains only a quarter of a wavelength in the pipe, giving λ=4L. Frequency is f=v/λ. The wave speed v is the same in both pipes, so the closed pipe has the larger wavelength (4L>2L) and consequently a lower frequency. In fact f_closed=f_open/2, so the closed pipe sounds a lower note.
Examiner tips
- State the boundary conditions for open and closed pipes
- Show the relation λ=2L or λ=4L for the fundamental
- Use f=v/λ to compare frequencies
- Mention that f_closed is half f_open
Common mistakes
- Confusing node and antinode positions
- Using λ=2L for both pipes
- Ignoring that f=v/λ, not λ=v/f
Mark scheme (4 marks)
- 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.
- 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.
- 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.
- 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 in this question
closed pipe · open pipe
Related
- All IB DP Physics Higher Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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