396 BELL SYSTEM TECHNICAL JOURNAL 



for 512 cycles so that these latter may be easily deduced for com- 

 parative purposes. These values are plotted to give curve number 4 

 in Fig. 4. It is seen that this curve agrees very well with those 

 showing the choices of competent judges. 



III. The Mork General Hypothesis 



Equation (2) may be written as follows, since we have assigned a 

 value to K: 



Ltdt = - 32.6 (6) 



L 



and it will be remembered that we have considered Li^ to be the loud- 

 ness set up by a certain standard source. Allowing V to vary with / 

 constant (1000 cycles) we have obtained a relation between the opti- 

 mum reverberation time and volume of rooms for 1000 cycles. We 

 wish to point out now that exactly this same condition (6) with V 

 constant and / variable, will give the same results that we have ob- 

 tained in Part I of this paper with the only further requirement that 

 for other frequencies than 1000 cycles the strength of the source E 

 shall be such that the loudness L/^ set up in the room at the frequency 

 considered shall be exactly the same as the loudness which our standard 

 source would set up at 1000 cycles. 



In Part I of this paper our stated condition was that the loudness of 

 all pure tones shall decay at the same rate for all frequencies. Since 

 we have specified that the loudness at the time /o shall be the same for 

 all test frequencies and also that the loudness at the time ti shall be 

 zero for all frequencies, it is quite evident that the above integral can 

 have the same value at all these frequencies only when the loudness 

 decays at the same rate for all frequencies concerned. In other words, 

 this condition stated as an integral specifies exactly the same require- 

 ment on the decay of loudness that we expressed in our statement early 

 in Part I of this paper. 



IV. Conclusions 



To recapitulate, we have set down an equation, together with a 

 specification of the strength of the virtual source in each case, from 

 which we obtain the value the reverberation time for any frequency 

 tone should have in any sized room according to the condition which 

 apparently controls the choice of observers. 



One naturally turns to see what meaning may be attached to this 

 significant expression, namely, the integral of the loudness taken 



