EFFICIENCY 153 



cycles coupled to the throat of a horn having a mechanical resistance of 1 

 ohm and an air chamber having a mechanical reactance of 1 ohm at 1000, 

 2000 and an infinite reactance for an initial efficiency of 20 per cent, 40 per 

 cent, 60 per cent, and 80 per cent. These characteristics are applicable 

 to other frequencies by multiplying the abscissa by any number and, of 

 course, multiplying the mass and the capacitance by the reciprocal of the 

 number. These characteristics are also applicable for other values of r 

 and m by simply multiplying these two factors by the same number and 

 the capacitance by the reciprocal of that number. The characteristics 

 shown in Fig. 8.4 have included mass, compliance products which cover the 

 useful range of values — larger products result in a peaked characteristic, 

 smaller values do not show much deviation from zero value of capacitance. 

 D. The Effect of the Generator Impedance and the Impedance at the 

 Throat of the Horn upon the Efficiency. — Due to the impracticability of 

 a horn mouth diameter comparable to the wavelength for low frequency 

 loud speakers, it is interesting to note that a relatively smooth output 

 characteristic can be obtained from a horn having an impedance char- 

 acteristic varying over wide limits. Near the cutoff of both finite and 

 infinite exponential horns the radiation resistance at the throat is small 

 and the positive reactance large. The compliance of the suspension sys- 

 tem should be chosen so that its capacitive reactance balances the posi- 

 tive reactance due to the throat. For example, consider a moving coil 

 mechanism coupled to the throat of a horn and fed by a vacuum tube 

 amplifier; the sound power output is the real part of 



Power = I , i I Zem 8.16 



where the motional resistance, in ohms, zem from equation 8.1, is 



{Biy 



A^{rAH +JXah) +JXm 



10- 



where B = air gap flux, in gausses, 



/ = length of wire in the voice coil, in centimeters, 

 A = area of the diaphragm, in square centimeters, 

 rAH = acoustic resistance at the throat, in acoustic ohms, 

 Xah = acoustic reactance at the throat, in acoustic ohms, and 

 Xm = mechanical reactance of the diaphragm, suspension and coil 

 system, in mechanical ohms. 



