Equations showing the relation between the volume, V, of an auditorium and its optimum reverberation time, T0, were published independently by MacNair and Lifschitz. MacNair's equation was derived from the following basic assumptions:
∫ 0T1 (logρ)dt = a const.
,
E = const.
, where
ρ=instantaneous value of the energy density of sound during decay,T1=time of decay to minimum audibility,E=rate of supply of energy during the steady state condition
.
This paper shows that an equation, relating T0 and V, can be deduced which more nearly fits all the empirical facts by basing the derivation on the following assumptions:
∫ 0T1 ρ ⋅ dt = a const.
,
E = GVn
, where
G=a constant,n=a constant which should be less than unity
.
The resulting equation for n = 23 is
T0 = 0.212 V1/6
. This is in agreement with the empirical data and with the equation derived by Maxfield and Albersheim from acoustic “liveness” considerations.

The psychologists and physiologists studying the mechanism of hearing should be interested in these results, as they have a bearing on the manner in which the ear integrates the sound being perceived.

Topics
Building acoustics, Architectural acoustics, Sound source perception
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© 1948 Acoustical Society of America.
1948
Acoustical Society of America
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