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BELL SYSTEM TECHNICAL JOURNAL 



is applied when the diaphragm has a normal velocity equal ^c'"' the 

 following boundary conditions are obtained: 



When X = 0, dcp/dx = — ^, 



X = h, d(p/dx = 0, 

 y = 0, d^ldy = 0, 



and when y = I, the pressure is equal to the product of acoustic 

 impedance and volume velocity or 



Fig. 11 — Schematic diagram of diaphragm and parallel slotted wall of infinite length. 



^r(^) jv^^rv-^^ dx 



h Jo V dt I y=i w J^ \ dy I y^i 



where <p is the velocity potential, k = oojc, and c is the velocity of 

 sound. 



The appropriate solution of equation (8) then is 



t 



cos ^v 



kh ( cos kl -]- i— sin kl 



w 



cos ^(.v — //.) 

 sin kh 



The average reacting force per unit area of the diaphragm is 



ikpc 



y- I (<p)x=o 



dy 



Thus, for the impedance per unit area, which is equal to the force 

 divided by the velocity, is obtained 



pd] 



w 



sin^ kl 



1 



cos2 kl-\- { -] sin2 kl 



It' 



-J 



.w 



kh cos kh 

 sin kh 



kl - 



sin kl cos kl 



h \2 

 COS' kl -\- [ — I sin' kl 



kH' 



Y^ r' + jx'. 



JJ 



