REGULAR COMBINATION OF ACOUSTIC ELEMENTS 



269 



What is generally desired is a knowledge of the effect produced by 

 inserting the filter in a given acoustic system. With the aid of 

 Thevenin's theorem, which is proved for an acoustic system in Appendix 

 I, and equations (20) and (21), this effect can be obtained. Thevenin's 



* 



Fig. 4 — Specific characteristic impedances for a low pass type of filter 



theorem states: If a source of simple harmonic pressure ;^o and of in- 

 ternal impedance 2^, per square centimeter, is connected to an acoustic 

 system, and if the specific impedance Zji terminates the system, the 

 volume velocity at the termination of the system will be Po'I\_{Zt'ISi) 

 + {ZiilS„)~\, where ^o' is the pressure at the terminating end when 

 this is closed through an infinite impedance, and Z^' is the impedance 

 per sq. cm. looking back into the acoustic system when this terminated 

 in the impedance Zj,. Si, and Sn are the areas at the input and output 

 junctions, respectively. 



Making use of Thevenin's theorem, the effect of inserting a filter in 

 a given system is the same as the effect obtained by inserting this filter 

 between a source of pressure po, with an internal impedance of ZjSi 

 and a terminating impedance Zb/Sn, where ZjSi and Zb/Sn are re- 

 spectively the total impedances looking toward the source, and away 

 from the source at the insertion junction of the acoustic system. We 

 have from equation (20) 



Fo = Vi cosh r - 



pi — pi. cosh r 



z. 



Si 



ih r. 



sinh r, 



