Open-Pipe Resonance: Length Sets the Pitch
1 · Predict
An open-open air column (like an open organ pipe) resonates at a fundamental frequency set by its length. If you use a shorter pipe, does the resonant pitch go up or down?
- A shorter pipe resonates at a higher fundamental frequency.
- A shorter pipe resonates at a lower fundamental frequency.
- Pipe length doesn't affect the fundamental frequency.
2 · Set Up
- Open the pipe-resonance preset and press Reset. The pipe is open at both ends, in 20°C air.
- Enable the fundamental-frequency readout on the pipe.
- Set the pipe length for each trial and record the fundamental frequency.
3 · Collect Data
| Pipe length L (m) | Fundamental wavelength λ (m) | Fundamental frequency f₁ (Hz) |
|---|---|---|
| 0.3 | ||
| 0.5 | ||
| 0.7 |
Plot fundamental frequency f₁ (y-axis) against 1/L (x-axis) for your three trials.
4 · Analyze
- For one trial, compute f₁ = c/(2L) using c = 331.3·√(1 + 20/273.15) m/s for 20°C air. Compare to the table.
- An open-open pipe's fundamental has a full wavelength λ = 2L. Explain, using v = fλ, why f₁ = c/(2L) follows directly from that wavelength.
5 · Extend
- A pipe closed at one end (like a clarinet) only supports odd harmonics and has fundamental f₁ = c/(4L) — half this experiment's frequency for the same length. Why might closing one end double the effective wavelength?
- The speed of sound c increases with air temperature. If you played this same pipe outdoors on a much colder day, would its resonant pitch go up or down? Why do wind instruments need retuning as temperature changes?
The Physics Behind This Experiment
Open-Pipe Fundamental
An air column open at both ends resonates with a full wavelength fitting twice its length (λ = 2L), giving fundamental frequency f₁ = c/(2L) — the same speed-wavelength relation as any wave, applied to sound in air.