REGULAR COMBINATION OF ACOUSTIC ELEMENTS 

 Hence we can express V2 in equation (73) as 



293 



F2 = 



Aft _|_ ^r 



which is Thevenin's theorem. 



Appendix II. Determination of Loss for a Constant 

 Volume Velocity Source 



Another type of insertion effect desired in some cases is the effect 

 caused by inserting filter structures in an acoustic system in which the 

 source suppHes a constant volume velocity. One such acoustic system 

 is the phonograph. 



In order to obtain this effect we first prove the theorem: If a 

 source of constant volume velocity Vi is connected to the input of an 

 acoustic system, and if the impedance Zr (per square centimeter) is 

 used to terminate the system, the volume velocity F2 will be 

 pQ"l[_{ZjilSi) + (Zc/5,)] where Pq" is the pressure at the termination of 

 the system when the system is closed through an infinite impedance, 

 and Zc is the specific impedance of the acoustic system at the output 

 junction looking toward the source when the system is terminated in 

 in an infinite impedance at the input junction, ^i and Sr, are the areas 

 at the input and output junctions, respectively. 



To prove this we substitute the value of pa given by (71) in the 

 first of equations (70) and obtain for the pressure, with an infinite im- 

 pedance termination 



.„_ V,Z, 



p2 — 



SiD 



(75) 



Then eliminating po from equations (70), and inserting the value 

 p2 = V^ZjilSr,, we obtain 



F2 



FiZo 



1 



Zj, AZo 



Sr, "^ S,D 



(76) 



From equation (74) we see that the impedance looking toward the 

 source is {ZqA/SjD) if we make Zj. approach infinity. Hence 



F2 = po 



1 



Zji . Zc 



S; 



