OPTIMUM REVERBERATION TIME FOR AUDITORIUMS 395 



where Top is the value of T imposed by our condition (2) for a thousand 

 cycle tone. 



Referring to Fig. 4 it will be seen that all three observers agree 

 rather closely that the reverberation time for an auditorium of 

 1,000,000 cubic feet should be 2.0 seconds. This value refers to a tone 

 of 512 cycles, the customary frequency used for experimental obser- 

 vation. It has been shown above that the reverberation time for 



8 



10,000 100,000 



VOLUME IN CUBIC FEET 



4 5 6 8 



l,000,000' 



Fig. 4. — Optimum reverberation time \s. volume in cubic feet for 512 cycles. 



1000 cycles should be 92.5 per cent of the reverberation time for a 

 512 cycle tone, so that the 2.0 seconds above corresponds to 1.85 

 seconds for 1000 cycles. We can evaluate K in (4) by adapting this 

 latter value of Top for a volume of 1,000,000 cubic feet. This 

 gives K = 32.6. Substituting this value in (4) we obtain 



6.35 



log V = 10.40 + log Top - 



T 1/2 

 ■* op 



(5) 



1,000 



4568 2 34568 



10,000 100,000 



VOLUME IN CUBIC FEET 



4 5 6 8 



1,000,000 



Fig. 5. — Optimum reverberation time vs. volume in cubic feet for 1000 cycles. 



From (5) we may obtain Top for 1000 cycles for any volume. See 

 Fig. 5. As mentioned above these values of Top are 92.5% of Top 



