OPTIMUM REVERBERATION TIME FOR AUDITORIUMS 393 



creases with the size of the room in the way shown in Fig. 4 where the 

 curves are the choices reported by Watson,^ Lifschitz,^ and Sabine.*' 

 These experimental results have served as the basis of successful 

 adjustment and design of many auditoriums. One naturally seeks 

 the factor which determines a choice of reverberation time of two 

 seconds for a million cubic feet theatre and on the other hand a choice 

 of near one second for a 10,000 cubic foot music room. It is our pur- 

 pose now to point out the factor which apparently does this. 



We will set down a condition which we believe to be this factor and 

 then will show that the requirements demanded by it agree quite 



10 



4568 2 34568 



100 1,000 



FREQUENCY IN CYCLES PER SECOND 



4 5 6 8 



10,000 



Fig. 3. — Relative number of absorption units vs. frequency. 



closely with the empirical results illustrated in Fig. 4 and mentioned 

 above. The condition is 





Ltdt = - K, 



(2) 



in which ^o is the time a sustained source of sound E is cut off, /i the 

 time the sound becomes inaudible, Lt the loudness of the sound at 

 any instant t, and K a constant. As shown in Fig. 1, the loudness of a 

 one thousand cycle note is equal to the sensation level, that is, 



Lt = Si for 1000 cycles. 



■•Watson, Architecture, May, 1927. 



* Lifschitz, Phys. Rev., 27, 618, 1926. 



« Sabine, Trans, of S.M.P.E., XII, 35, 1928. 



