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.
- 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
Frequently Asked Questions
Why do closed pipes only have odd harmonics?
A closed end must be a displacement node and an open end must be an antinode. This boundary condition only supports odd-numbered harmonics.
What is the fundamental frequency?
The fundamental is the lowest resonant frequency (n = 1), also called the first harmonic.
How do organ pipes produce different notes?
By varying pipe length. Longer pipes produce lower frequencies, shorter pipes produce higher frequencies.
Ready to run the numbers?
Open Resonance Frequency Calculator