C.4 · IB Physics
Standing waves in pipes
Compare a pipe closed at one end with a pipe open at both ends. See the first four possible harmonics as displacement patterns, with nodes (N) and antinodes (A), and how their wavelengths and frequencies depend on pipe length and the speed of sound.
| n | λ / m | f / Hz |
|---|
Try this
- Closed pipe, L = 0.85 m, v = 340 m s⁻¹: confirm the fundamental is 100 Hz and that the next possible frequency is 300 Hz, not 200 Hz.
- Keep L = 0.85 m and switch to open at both ends: how do the fundamental wavelength and frequency change? Explain using quarter and half wavelengths.
- Raise v from 330 to 350 m s⁻¹ (warmer air) at fixed length: note that every λ stays the same while every f rises by the same factor.
Exam tip: when sketching displacement patterns, always put a node at a closed end and an antinode at an open end, then fit whole quarter-wavelengths into L, so a closed pipe gives L = nλ/4 with n odd only.