Page 209 - Master Handbook of Acoustics

the significance of double-slope phenomena (see Fig. 9-2) is revealed only near the end of the decay.
In practice, the highest amplitude of sound source reasonably attainable is used, and filters can be
incorporated to improve the signal-to-noise ratio of the measurement.

Sabine Equation

Sabine’s reverberation equation, published in 1900, was developed in a strictly empirical fashion.
He had two lecture halls at his disposal, and by adding or removing seat cushions of a uniform kind,
he was able to clarify the role of absorption in room reverberation. He observed that reverberation
time depends on room volume, and absorption. The greater the absorption, the shorter the
reverberation time. Likewise, the greater the room volume, the longer the reverberation time because
sound will strike the absorbing room boundaries less often.

The quantity 4V/S describes the average distance a sound travels between two successive
reflections; it is sometimes called the mean free path. In the equation, V is the room volume, and S is
the room surface area. For example, consider a room measuring 23.3 ×16 ×10 ft. The volume is 3,728
3
2
ft and the surface area is 1,533 ft . The mean free path for this room is 4V/S or (4)(3,728)/1,533 =
9.7 ft. Since the speed of sound is 1,130 ft/sec, on average a sound ray will travel 8.5 msec before
striking another room surface. It might take between four to six reflections before the sound energy in
this sound ray is mainly lost, a decay process that will take 42.5 msec. But the number of bounces
actually required will depend on how absorptive the room is. For example, the decay process will
require more bounces in a live room, and thus take longer. In addition, because the mean free path is
longer in large rooms, the decay process will take longer in large rooms.

Using this kind of statistical theory and geometrical ray acoustics, Sabine devised his equation for
room reverberation. In particular, he devised the following relationship:

where RT =
60
reverberation time, sec
V =

volume of room, ft 3
A =
total absorption of room, sabins

The Sabine equation can also be expressed in metric units:

where RT =
60
reverberation time, sec
V =

volume of room, m 3
A =