Acoustic Resonance Calculator Formula

Understand the math behind the acoustic resonance calculator. Each variable explained with a worked example.

Use the Acoustic Resonance Calculator

Formulas Used

Resonant Frequency

resonant_freq = (343 / 2) * sqrt(pow(nx / length, 2) + pow(ny / width, 2) + pow(nz / height, 2))

Variables

VariableDescriptionDefault
lengthRoom Length (Lx)(m)8
widthRoom Width (Ly)(m)5
heightRoom Height (Lz)(m)3
nxMode Number nx1
nyMode Number ny0
nzMode Number nz0

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)

  • *c* = 343 m/s (speed of sound in air)
  • *Lx, Ly, Lz* = room dimensions
  • *nx, ny, nz* = mode numbers (non-negative integers, not all zero)

    • 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).

    length = 8width = 5height = 3nx = 1ny = 0nz = 0
    1. 01f = (343/2) * sqrt((1/8)^2 + 0 + 0)
    2. 02f = 171.5 * sqrt(0.015625)
    3. 03f = 171.5 * 0.125
    4. 04f = 21.44 Hz

    Ready to run the numbers?

    Open Acoustic Resonance Calculator