274 DYNAMICAL THEORY OF SOUND 



should, under the given conditions, be so much greater than 

 in the preceding case is due to the relatively smaller efficiency 

 of a double source, as compared with a simple one, in propagating 

 energy outwards ( 80). 



It may be well to insist again that the increased output 

 of energy is an indirect consequence of the presence of the 

 resonator, which itself does no work. The whole energy is 

 supplied by the original source, where the motion takes place 

 against an augmented component of pressure in the same phase 

 with the velocity. The velocity-potential due to the flux q 

 outwards from the resonator, as given by (11), is 



<>, = sin (nt kr e), (17) 



kr 



and the resultant pressure is 



P=PQ-\ cos (nt kr e). (1$) 



r 



In the case of a simple primary source we had J=A/4>7rb ) 

 e = kb; hence, putting r = b, we find that the consequent 

 pressure in the neighbourhood of this source is 



(19) 



Since the imposed outward flux is A cos nt, the mean rate of 

 work against this part of the pressure is 



The output is therefore greater than it would be in the 

 absence of the resonator, in the ratio cos 2kb/k 2 b 2 . This agrees 

 with the former result, obtained on the hypothesis that kb is 

 small. 



The energy stored in the resonator under the conditions of 

 maximum vibration is, by 86 (15), 



E = 8 



This varies directly as the capacity Q, and is for apertures of 

 similar form inversely proportional to the area. 



The effect of a resonator under the influence of a distant 



