150 HORN LOUD SPEAKERS 



where Tm = resistive component of the vibrating system, in mechanical 

 ohms, and 

 Xm = reactive component of the vibrating system, in mechanical 

 ohms. 

 In this discussion, let 



Xm = 0) (mo + mc) 8.11 



At the high frequencies the reactance due to Cms and Xma is negligible 

 compared to the reactance due to the mass of the diaphragm. In order 

 to divorce the effect of the air chamber from the effect of the mass of the 

 diaphragm, the capacitance Cai will be assumed to be zero. For the same 

 reason Tma will be assumed to be zero. These effects will be considered in 

 following sections. The mechanical resistance Tm then becomes the horn 

 throat resistance rMH- The throat mechanical resistance is given by 



Tmh = 42Jt 8.12 



where /fr = area of the throat, in square centimeters. Substituting 

 equation 8.10 in 8.2, the efficiency becomes 



^ (Biy-rMH 



^ VEDifMH' + Xm')\0' + {BIYTmH 



This expression shows that the efficiency is a function of the flux density, 

 the coil mass and material, the diaphragm mass, the throat resistance and 

 the frequency. The efficiency characteristics for ratios of voice coil mass 

 to diaphragm mass of 1 : 1 and 1 : 2, and flux densities of 22,000, 14,000 

 gausses for an aluminum voice coil is shown in Fig. 8.3. The character- 

 istics of Fig. 8.3 are applicable to a copper voice coil by multiplying the 

 abscissa by 0.5. In order to connect with the characteristics of initial effi- 

 ciency of Fig. 8.2, these curves are depicted in terms of the initial efficiency 

 (20, 40, 60, and 80 per cent). This data shows that it is comparatively 

 simple to obtain high efficiencies at the lower frequencies. However, at 

 the higher frequencies the efficiency is limited by the mass of the diaphragm 

 and voice coil. 



C. The Effect of the Air Chamber upon the Efficiency ic n- 12, i3, i4_ — 'X\\s. 

 result of the preceding sections were obtained by assuming the capacitance 



loHanna and Slepian, Jour. A.I.E.E., Vol. 42, No. 3, p. 251, 1924. 



" Wente and Thuras, Bell Syst. Tech. Jour., Vol. 7, No. 1, p. 140, 1928. 



12 Olson, H. F., Jour. Acous. Sac. Amer. Vol. 2, No. 4, p. 242, 1931. 



13 Wente and Thuras, Jour. AA.E.E., Vol. 53, No. 1, p. 17, 1934. 

 " Olson, H. F., RCA Review, Vol. 2, No. 2, p. 265, 1937. 



