292 BELL SYSTEM TECHNICAL JOURNAL 



pressure po, whose specific internal impedance is Z^, we can write 



po= pi-\- Vi 



5i 



Inserting this result in the above equation, we obtain 



Fi 



PoA -^(ZrA + ZoB), 



V2= Vr(C + ^D)- 



poSi 



D. 



(70) 



To obtain the pressure when an infinite impedance is used at the 

 termination, we let V2 = 0, and solving for Vi we have 



Fi 



poDSi 



ZoC + ZtD 



Substituting this in the first of equations (70), we have 



poZo 



p2 



{ZoC + ZrD) 



Po, 



(71) 



(72) 



which is the terminal pressure for an infinite terminating impedance. 

 Eliminating Vi from (70) and substituting ¥2^2^/8,, — po, we have 



Vo 



poZo 



X 



1 



{ZoC + ZrD) Z^,Zo/ ZtA + ZqB 

 Sr,^ S\ ZoC + ZtD 



(73) 



We can show now that 



Zo ( ZtA -|- ZoB 



Si \ ZoC + ZtD 





which is the impedance at the terminating junction looking toward the 

 source, when the specific impedance Zt terminates the input end- 

 From equations (63) and (64), we can write 



p^'^Pi'C - F/%5, 



Zo 



Substituting F2'(Zr/5i) = P-i and solving for the ratio pi'/Vi, we have 

 pi _ Zt _ Zo ( ZtA + ZoB \ (TA\ 



Fi' Si Si \ ZoC + ZtD 



