Acoustic modes computation

What are acoustic modes for a cavity?

A natural acoustic mode of a box is a standing pressure wave that fits exactly in the box.
For example take a pan flute tube, open at one end, closed at the other. In the following graph you can change the wavelenght and the time instant of -let’s say- a standing pressure wave. The graph will tell you when your wave is at the same time:

• 0 at left (no pressure fluctuation, for an open end)
• and 1 or -1 at right (maximum pressure fluctuation, for a closed end).

These are the acoustic modes of your pan flute. Fiddle with the wavelength to catch all the modes.

Change the wavelenght:

Change the instant:

Using the equations of acoustics we can directly estimate the wavelenght and frequency of the natural modes for simple shapes. See here the natural modes of a box and a cylinder.

Acoustic modes of a closed box

Speed of sound (m/s)

X size (m)

Y size (m)

Z size (m)

Results:

The volume of the box is 0.050265 m3.
Mode 1.0.0 : 422.000000 Hz
Mode 2.0.0 : 844.000000 Hz
Mode 3.0.0 : 1266.000000 Hz
Mode 0.1.0 : 4220.000000 Hz
Mode 0.0.1 : 2110.000000 Hz
Mode 0.1.1 : 4718.103433 Hz
Mode 1.1.0 : 4241.047512 Hz
Mode 1.0.1 : 2151.786235 Hz
Mode 1.1.1 : 4736.938252 Hz

Acoustic modes of a closed cylinder

Speed of sound (m/s)
X size (m)
Radius (m)

Results:

The volume of the cylinder is 0.050265 m3.
Mode 1.0.0 : 450.000000 Hz
Mode 2.0.0 : 900.000000 Hz
Mode 3.0.0 : 1350.000000 Hz
Mode 0.0.1 : 527.400000 Hz
Mode 0.1.0 : 1098.000000 Hz
Mode 0.1.1 : 1527.300000 Hz
Mode 1.0.1 : 693.289810 Hz
Mode 1.1.0 : 1186.635580 Hz
Mode 1.1.1 : 1592.213959 Hz