112 DIRECT RADIATOR LOUD SPEAKERS 



a single mechanism may be designed to yield uniform response to the upper 

 limit of audibility. 



It is the purpose of this chapter to outline the factors which influence 

 the performance of the conventional direct radiator loud speaker, to illus- 

 trate systems for controlling the response with respect to frequency and to 

 describe several means for decreasing the effective mass of the vibrating 

 systems at the high frequencies and for improving the efficiency at the low 

 frequencies. 



7.2. Single Coil, Single Cone Loud Speaker^ — The simple dynamic 

 loud speaker consists of a paper cone driven by a voice coil located in 

 a magnetic field. The mechanical impedance of this arrangement is 

 given by 



'Zmt = fMC +JXmc + rMA -\-JXma 7.1 



where Tmc = mechanical resistance in the diaphragm, in mechanical ohms, 

 Xmc = mechanical reactance of the cone and coil, in mechanical 



ohms, 

 f'MA = mechanical resistance due to the air load, in mechanical ohms, 



and 

 Xma = mechanical reactance due to the air load, in mechanical ohms. 

 The efficiency, in per cent, of this loud speaker may be expressed as 



{Biyir-MC + Vma) + tedWhc + rinAY + (xma + ^mc)^110^ 



where ted = resistance of the voice coil, in ohms, 



/ = length of the conductor of the voice coil, in centimeters, and 

 B = flux density in the air gap, in gausses. 

 In general rue is small and may be neglected. If ruA is small com- 

 pared to Xma and Xmc, equation 7.2 becomes 



rED{XMA + ^MC) "10'' 



In terms of the resistivity and density of the voice coil the efficiency, in 

 per cent, is 



pkr{XMA + XMCrlO^ 



1 Olson, H. F., Jour. Acous. Soc. Amer., Vol. 10, No. 4, p. 305, 1939. 



