RECORDING AND REPRODUCING OF MUSIC AND SPEECH 507 



however, are either standard in the literature or may always be 

 reduced to those given above. 



As illustrations of the general methods employed certain important 

 portions of the reproducer will be considered in detail. Considering 

 first the electrical analog of the air chamber ^ between the diaphragm 

 and horn, we make use of the following list of svmbols (see Figs. 

 3, 4, 15 and 16) : 



W3 = Effective mass of diaphragm in grams; 

 ^ 1 = Equivalent area of diaphragm in cms^; 

 Ce = Compliance of edge of diaphragm; 

 C7 = Compliance of air chamber; 

 yl2= Area of throat of horn; 

 Zh = Impedance of horn— \'ector ratio of applied force at the throat 



of the horn to the resultant linear velocity of the air; 

 Si = Displacement of diaphragm; 

 t'i= Velocity of diaphragm; 

 52 = Displacement of air in throat of horn; 

 z'2 = Velocity of air in throat of horn; 

 Pq and Fo = Initial pressure and volume of air-chamber; 

 F = Force applied to diaphragm; 

 p = Small change of pressure in air-chamber. 

 For a small change p in the pressure within the air-chamber we have : 



^= Vo (1) 



where w = l for an isothermal change and 1.4 for an adiabatic change. 

 For the case under consideration « = 1.4 very nearly. 



If the horn opening is closed, 5? = 0, and we get for the compliance 

 of the air chamber as measured from the diaphragm 



c - '' - ^« 

 ^ pA 1 npoA i2 



We have the two force equations 



ZhV2-pA2 = (3) 



' The use of the air chamber to increase the loading effect of the horn on the 

 diaphragm has been appreciated for a number of years. It has been used in tele- 

 phone receivers, phonographs, and loud speaking receivers since their earliest devel- 

 opments. A treatment of the force equations of the air-chamber was given by 

 Hanna & Slepian, "The Function and Design of Horns for Loud Speakers." Trans. 

 A. I. E. E., 1924, p. 393. The equivalent structure, however, was analysed as a 

 compliance and resistance in series instead of in shunt. 



