REGULAR COMBINATION OF ACOUSTIC ELEMENTS 291 



From (63) eliminating the ratio Vr,'IVi and writing pr,'IVj,' = ZjJSi 

 and pi'lVi — ZiJSr, and substituting the vahies in (64), we have 



Z^.ZjP + Zo, lZj.,C- Zj, I; ^ ) - Z,:- j^B = 0. (66) 



Solving (65) and (66) simultaneously, we find 



From the definition of 6 and equations (62), we can show that 



cosh d - ^1AC. (68) 



In terms of these parameters, the effect upon the pressure or volume 

 velocity in the termination of an acoustic system, due to inserting the 

 structure into the system, will be given by multiplying the terminal 

 pressure or volume velocity by the factor 



2Zfl Zj^ + Zji Zj.^ -\- Zg 



Sr, (69) 



1 

 X 



1 _ ^^' ^B y ^/i ^A y 2fl 



where Z^ and Z^ are respectively the impedances, per square centi- 

 meter, of the acoustic system at the insertion junction looking towards 

 and away from the source. 



Appendix I. Proof of Thevenin's Theorem for an Acoustic 



System 



The proof of Thevenin's theorem as stated in Section III can be 

 obtained directly from the general network equations given in Section 

 V. These equations are 



Zo 

 where AC — BD — 1. If we connect at the input end a source of 



