Subwoofer tools.
SYSTEM PLANNING / THE TOOLKIT

Room modes.

List the ideal rigid-wall modes of a rectangular room. These are frequencies to investigate, not predictions of how large a peak will be at your listening seat.

01 / THE INPUTS
Room dimensions
Frequency range
Hz

Up to 500 Hz. Enumeration is limited to 500,000 candidate modes.

Optional pressure pattern
Air & conventions
m/s
kg/m3
02 / THE RESULTS
Ideal modes in range
33modes
First length axial mode
34.3Hz
First width axial mode
42.9Hz
First height axial mode
68.6Hz

Ideal rigid-wall modal frequencies

FREQUENCY
Ideal rigid-wall modal frequencies: Mode occurrence against frequency in hertz.00.220.430.650.861.0834.357.3980.48103.57126.66149.76Mode occurrenceFrequency (Hz)

All modes in the selected range

Frequency (Hz)Indices (n, m, p)Classification
34.301, 0, 0Axial
42.880, 1, 0Axial
54.911, 1, 0Tangential
68.600, 0, 1Axial
68.602, 0, 0Axial
76.701, 0, 1Tangential
80.900, 1, 1Tangential
80.902, 1, 0Tangential
85.750, 2, 0Axial
87.871, 1, 1Oblique
92.361, 2, 0Tangential
97.022, 0, 1Tangential
102.903, 0, 0Axial
106.072, 1, 1Oblique
109.810, 2, 1Tangential
109.812, 2, 0Tangential
111.483, 1, 0Tangential
115.051, 2, 1Oblique
123.673, 0, 1Tangential
128.630, 3, 0Axial
129.482, 2, 1Oblique
130.893, 1, 1Oblique
133.121, 3, 0Tangential
133.953, 2, 0Tangential
137.200, 0, 2Axial
1-25 of 33
Page 1 of 2

Read this result with its assumptions.

Axial: one nonzero index. Tangential: two. Oblique: three. Degenerate modes are retained separately.

The vertical stems mark frequencies, not predicted response amplitudes.

Rigid rectangular boundaries only. Real-room losses, openings, furnishings, and placement change the response.

Units & assumptions

Your calculations run in this browser. No account needed.

03 / UNDER THE HOOD

The math, in plain sight.

Get to know the room around your subwoofer.

Frequencies in a rectangular rigid-walled room

Let n, m, and p be nonnegative integers, not all zero. One nonzero index is axial, two are tangential, and three are oblique.

fnmp=c2(nL)2+(mW)2+(pH)2f_{nmp}=\frac c2\sqrt{\left(\frac nL\right)^2+\left(\frac mW\right)^2+\left(\frac pH\right)^2}

Ideal relative pressure pattern

The optional pressure value is signed and normalized to the ideal modal pattern. It does not determine excitation strength, damping, or the actual combined response at a seat.

Pnmp(x,y,z)∝cos⁡(nπxL)cos⁡(mπyW)cos⁡(pπzH)P_{nmp}(x,y,z)\propto\cos\left(\frac{n\pi x}L\right)\cos\left(\frac{m\pi y}W\right)\cos\left(\frac{p\pi z}H\right)

Worked example

A 5.0 x 4.0 x 2.5 m room at 343 m/s has first axial frequencies of approximately 34.3 Hz, 42.9 Hz, and 68.6 Hz.

These are possible modal frequencies, not predicted peaks of a specified size. Openings, flexible surfaces, furnishings, source and listener placement, and losses all change the measured response.