Cavity Acoustics

The acoustics of enclosed volumes are important when considering sound propagation within the volume. The acoustic modes will "colour" the sound, ie enhance certain frequencies and dull others. The acoustic modes will be dependent on the enclosure dimensions and for a simple rectangular cavity the frequency of a mode is given by:
where
c0 = speed of sound [ms-1]
l, m, n = 0, 1, 2, 3, ......
Lx, Ly, Lz = room dimensions in each direction [m]

The modal density has been approximated by the follwing equations for each dimension of the cavity from the simple 1 dimensional tube to the 3 dimensional volume.

Modal density of a tube

Modal density of a shallow cavity

Modal density of a volume

A more exact expression for a volume that includes additional terms at low frequencies is:
This approximation is shown below compared to the exact solution that was determined by calculating the exact frequency for each mode.

Modal density shown based on different calculation methods for Lx=3.0m, Ly=0.4m, Lz=0.1m, c=343ms-1

Direct and Reverberant Sound
where
Π = sound power [W]

For a noise pulse to be transmitted in a room without serious distortion of shape there must be an adequate number of standing waves with frequencies within a frequency band. An adequate number of modes is usually about 10. The lower and upper limits of the band are defined by:
and

See also: Axial Mode, Room Modes, Sound.

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Subjects: Architectural Acoustics Noise & Vibration