optimum Reverberation Time for Auditoriums 



By WALTER A. MAC N AIR i 



The suggestion is made that the sound damping material in an auditorium 

 should be such that the loudness of tones will decay at the same rate for all 

 frequencies. To attain this the reverberation time at 80 cycles must be 

 twice what it is at 1000 cycles. 



The change of optimum reverberation time with volume is shown to be 

 derivable from a single hypothesis. 



I. Reverberation Time vs. Frequency 



THERE is very little published data in regard to the change in 

 reverberation time with frequency in auditoriums which are 

 considered near ideal. It is often mentioned by engineers and physi- 

 cists that to secure the best acoustical results, the reverberation time 

 should be the same for all frequencies in any one room. This specifies 

 that the sensation level shall decay at the same rate for all frequencies 

 of interest. 



It seems more reasonable, however, to specify that the loudness of all 

 pure tones shall decay at the same rate for all frequencies since it is the 

 loudness of a tone which takes into consideration not only the energy 

 level but also its ultimate effect upon one's brain. In Fig. 1 - are 

 plotted data which show the relation between the loudness as judged 

 by a considerable number of observers and the sensation level. It 

 will be seen that for frequencies between 700 and 4000 cycles per 

 second these two quantities are equal to each other so that the two 

 points of view mentioned above demand identical conditions through- 

 out this frequency band. Outside of this band, however, any change 

 in the sensation level gives a greater change in the loudness, as may 

 be seen. 



The maximum loudness in which we are interested at present is about 

 73.^ In the figure the curves may be replaced by straight lines which 

 represent fair approximations to the observed data up to this loudness. 

 This family of straight lines may be represented by the expression 



Lt = AfSu (1) 



where Aj \s the slope of the line adopted to fit the data for the fre- 



1 Presented before Acoustical Soc. of Amer., Dec, 1929. Jour. Acou. Soc. Amer., 

 Jan., 1930. 



-This is Fig. 108 from "Speech and Hearing" by H. Fletcher. 

 ^ This is the loudness that the source chosen in Part II of this paper will produce 

 in a room of 1000 cubic feet having a reverberation time of 0.8 seconds. 



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