Resonance Frequency Calculator Formula
Understand the math behind the resonance frequency calculator. Each variable explained with a worked example.
Formulas Used
Open Pipe Frequency
open_freq = harmonic * sound_speed / (2 * pipe_length)Closed Pipe Frequency (odd n)
closed_freq = harmonic * sound_speed / (4 * pipe_length)Variables
| Variable | Description | Default |
|---|---|---|
harmonic | Harmonic Number (n) | 1 |
sound_speed | Speed of Sound(m/s) | 343 |
pipe_length | Pipe Length(m) | 0.5 |
How It Works
Resonance in Pipes
Standing waves form in pipes at specific frequencies determined by the pipe length and boundary conditions.
Open Pipe (both ends open)
f_n = n * v / (2L) where n = 1, 2, 3, ...
Closed Pipe (one end closed)
f_n = n * v / (4L) where n = 1, 3, 5, ... (odd harmonics only)
Worked Example
Fundamental frequency of a 0.5 m open pipe at 343 m/s.
harmonic = 1sound_speed = 343pipe_length = 0.5
- 01f_open = n * v / (2L)
- 02f_open = 1 * 343 / (2 * 0.5)
- 03f_open = 343 Hz
- 04f_closed = 1 * 343 / (4 * 0.5)
- 05f_closed = 171.5 Hz
Ready to run the numbers?
Open Resonance Frequency Calculator