Calculator Inputs
Formula Used
This calculator uses an effective length model: Leff = L + Nopen · k · r, where r is the inner radius, k is the end factor, and Nopen is the number of open ends.
- Open–Open (or Closed–Closed): fn = n · v / (2 Leff)
- Open–Closed: fn = (2n−1) · v / (4 Leff) (odd orders only)
- Wavelength: λ = v / f
Temperature mode estimates sound speed with v ≈ 331.3 + 0.606·T (m/s), where T is in °C.
How to Use This Calculator
- Pick the pipe end condition that matches your setup.
- Enter pipe length and choose the correct unit.
- Enable end correction, then provide the inner diameter.
- Select temperature mode or enter a custom sound speed.
- Choose how many modes to list, then calculate.
- Export the table when you need a clean file.
Example Data Table
| Scenario | Pipe type | Length (m) | Diameter (m) | Temp (°C) | Fundamental (Hz) |
|---|---|---|---|---|---|
| Classroom tube | Open–Open | 1.000 | 0.050 | 20 | 166.628 |
| Resonance demo | Open–Closed | 0.800 | 0.030 | 25 | 107.041 |
| Sealed column | Closed–Closed | 0.500 | 0.000 | 20 | 343.420 |
FAQs
1) What is pipe resonance?
It is the set of standing-wave frequencies that fit inside a pipe. Resonance occurs when reflections at the ends reinforce the wave, creating nodes and antinodes at predictable positions.
2) Why do open–closed pipes show odd harmonics?
One end must be a displacement node (closed) and the other an antinode (open). That boundary pairing only supports quarter-wave patterns, producing harmonic orders 1, 3, 5, and so on.
3) What does end correction change?
Air motion extends slightly beyond an open end, making the resonating air column effectively longer. Adding k·r per open end lowers predicted frequencies, especially for short or wide pipes.
4) Do I need diameter for every case?
Only when end correction is enabled and the pipe has an open end. Closed–closed pipes have no open ends, so the simple end-correction model adds nothing.
5) How does temperature affect the results?
Higher air temperature increases the speed of sound, which increases every resonance frequency. If your lab is warm or cold, temperature mode is an easy way to capture this change.
6) Which length should I measure?
Use the physical tube length between end faces. If the pipe opens into a large space or has fittings, the effective length may differ; end correction helps, but complex geometries may need more detailed acoustics models.
7) Why don’t my measured frequencies match perfectly?
Real pipes include losses, wall compliance, non-ideal end shapes, and humidity effects. Microphones and excitation methods also matter. Treat results as strong estimates unless you calibrate with measurements.
8) What should I do if the calculator shows an error?
Check that length is positive, and enter a diameter when end correction is enabled for open ends. Also confirm temperature mode has a reasonable temperature, or manual mode has a positive sound speed.