DISPERSION OF SOUND 279 



12.2. Dispersion of Sound i- 2- 3- ^^ ^ ^ — A. Sound Absorption and Re- 

 verberation. — When a source of sound is started in a room the energy does 

 not build up instantly due to the finite velocity of a sound wave. Each 

 pencil of sound sent out by the source is reflected many times from the 

 absorbing walls of the room before it is ultimately dissipated. A steady 

 state condition obtains when the energy absorbed by the walls equals the 

 energy delivered by the sound source. In the same way, when the source 

 is stopped, some time is required before the energy in the room is com- 

 pletely absorbed. The reverberation time has been arbitrarily defined 

 by Sabine as the time required for the sound to decrease to one millionth 

 of its original intensity after stopping the source. 



The equation ^ for the decay of the sound in a room is 



E = £oe-«^'/4^ ^ 12.1 



where E = sound energy density, after a time / seconds, after stopping the 

 source, in ergs per cubic foot, 

 A = total number of absorption units, in sabins (see definition 



below), 

 £o = ^Po/cA, 



Pq = rate at which sound is generated by the source, in ergs per 

 second, 

 c = velocity of sound, in feet per second, and 

 V = volume of the room, in cubic feet. 

 The acoustic absorptivity (or absorption coefficient) of a surface is the 

 ratio of the flow of sound energy into the surface on the side of incidence 

 to the incident rate of flow. The sabin is a unit of equivalent absorption 

 and is equal to the equivalent absorption of one square foot of a surface 

 of unit absorptivity, that is, of one square foot of surface which absorbs 

 all incident sound energy. 



From equation 12.1 the time required for the sound to decay to one 



^ Sabine, W. C, " Collected Papers in Acoustics," Harvard Uni. Press, Cam- 

 bridge, Mass. 



2 Watson, F. R., " Acoustics of Buildings," John Wiley and Sons, New York, 1923. 



^ Begenal and Wood, " Planning for Good Acoustics," Methuen, 1931. 



* Knudsen, V. O., " Architectural Acoustics," John Wiley and Sons, New York, 

 1932. 



^ Sabine, P. E., " Acoustics and Architecture," McGraw Hill Book Co., New 

 York, 1932. 



^ Olson and Massa, " Applied Acoustics," 2nd Ed., P. Blakiston's Son and Co., 

 Philadelphia, 1939. 



7 Franklin, W. S., Phys. Rev., Vol. 16, p. 372, 1903. 



