Acoustic Resonance Calculator Formula
Understand the math behind the acoustic resonance calculator. Each variable explained with a worked example.
Formulas Used
Resonant Frequency
resonant_freq = (343 / 2) * sqrt(pow(nx / length, 2) + pow(ny / width, 2) + pow(nz / height, 2))Variables
| Variable | Description | Default |
|---|---|---|
length | Room Length (Lx)(m) | 8 |
width | Room Width (Ly)(m) | 5 |
height | Room Height (Lz)(m) | 3 |
nx | Mode Number nx | 1 |
ny | Mode Number ny | 0 |
nz | Mode Number nz | 0 |
How It Works
Room Acoustic Modes
A rectangular room supports standing waves at specific resonant frequencies determined by its dimensions.
Formula
f(nx,ny,nz) = (c/2) sqrt((nx/Lx)^2 + (ny/Ly)^2 + (nz/Lz)^2)
Axial modes (one non-zero index) are strongest. Tangential (two) and oblique (three) modes are progressively weaker.
Worked Example
Room 8 x 5 x 3 m, first axial mode along length (1,0,0).
- 01f = (343/2) * sqrt((1/8)^2 + 0 + 0)
- 02f = 171.5 * sqrt(0.015625)
- 03f = 171.5 * 0.125
- 04f = 21.44 Hz
Frequently Asked Questions
Why do room modes cause problems?
At resonant frequencies, sound builds up at certain positions and cancels at others, creating uneven bass response. This is why studio control rooms use non-parallel walls or bass traps.
What are the ideal room dimension ratios?
Ratios like 1:1.26:1.59 or 1:1.4:1.9 (from Bolt or Louden criteria) distribute modes more evenly, avoiding clustering of resonances.
Can room modes be eliminated?
No, but they can be managed with bass traps (absorption at room boundaries), equalization, and choosing good room proportions.
Ready to run the numbers?
Open Acoustic Resonance Calculator