ARCHITECTURAL ACOUSTICS 109 



every ray will experience the same number of reflections per 

 second, a number dependent on the size and the shape of the 

 room. Applying statistical methods, Jager shows that the 

 maximum energy density, i.e. the maximum intensity attained, 

 is given by : 



F - 4A 

 ^» avS' 

 where A = energy emitted per second. 



a = average absorbing power of the surfaces present. 



V = velocity of sound. 



S = total surface, including irregularities. 

 A being constant, E^ is greater for small values of a and S. 

 Breaking up the walls by introducing irregularities tends to 

 decrease the intensity attained. The removal or introduction 

 of furnishings changes not only S, but also the average value of 

 a. To find the effect on the intensity the change in aS must 

 be observed. 



We have already seen that 



aS = flj Sj + ttj Sg + . . . , 

 hence it is clear that the maximum intensity attained is always 

 weakened by introducing objects, including people. 



When the sound has attained its maximum intensity £„ its 



— atiS, 



intensity E at a time / afterwards is given by E = E^ e 4V ' 

 where e is the exponential and V the volume of the room. 

 This formula is the same in effect as Franklin's. The greater 

 the absolute value of the exponent the quicker the decay. 

 Since V cannot be altered without at the same time altering S, 



. S . . . 

 it is the ratio ^^ which is important in determining the rever- 

 beration. Hence the effect of extensive diversification of the 

 walls is to reduce the time of reverberation. With increasing 



S 

 volume ^ always decreases. Hence increasing volume has the 



effect of increasing the time of reverberation. 



S . . 

 The dependence of reverberation on ^ is an important point 



to note, for it shows that two auditoriums of exactly the same 

 shape and constructed of similar materials do not have the same 

 acoustical properties unless they are of the same size. 

 The formula 



4V'' 



shows that rooms acoustically good are restricted in dimensions. 

 The desiderata are a fixed intensity of sound and a short period 

 of reverberation. 



