Sabine reverberation equation revisited.

Abstract

About 1900 W. C. Sabine reported the ‘‘sound absorbing power’’ of materials in a reverberant room as proportional to a logarithm of the ratio of an initial to a final ‘‘residual sound,’’ after the source is stopped. In present-day terms, sound pressure level (a logarithm) decays at the rate d decibels per second, after the source is stopped. At least as far back as 1965, ASTM C423, ‘‘Sound Absorption⋅⋅⋅Reverberation Room Method,’’ obtained the Sabine absorption A in metric sabins by A=0.9210 Vd/c; 0.4 ln 10=0.9210 is a pure number. The volume of the reverberation room is V, cubic meters; the speed of sound of air therein is c, meters per second. On substituting reverberation time T=60 dB/d, Sabine sound absorption A=55.3(dB)V/cT; this dimensionally complete equation shows the decibel explicitly. The Sabine absorption of a surface of area S in square meters, and Sabine absorption coefficient a, isA=Sa. The unit of the Sabine coefficient a is thus the decibel; it is dimensionless in the sense of length, mass, or time; the unit is usually omitted. Being derived from a decay rate, the Sabine sound absorption coefficient is not ‘‘Ideally the fraction of the randomly incident sound power absorbed... .’’