NONLINEAR DISTORTION 



159 



A = projected area of the air chamber upon the diaphragm, in square 



centimeters, 

 d! = distance between the diaphragm and front boundary of the air 



chamber in the absence of motion, in centimeters, and 

 X = displacement of the diaphragm, in centimeters. 

 The equivalent circuit of the mechanical system shows the effect of the 

 nonlinear element upon the sound power output. In the case of a single 

 frequency the distortion which this element introduces is small, because 

 for constant sound power output the amplitude of the diaphragm is inversely 

 proportional to the frequency. At low frequencies where the amplitude 



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EQUIVALENT CIRCUIT 



DIAPHRAGM 



ELECTRIC INPUT ACOUSTIC OUTPUT 



LOW FREQUENCY 



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HIGH FREQUENCY 



■ai OUTPUT 



VOICE 

 COIL 

 LEADS' 



COMBINATION HIGH AND LOW FREQUENCY 



FIELD COIL 



^VOICE COIL 

 CROSS-SECTIONAL VIEW 



Fig. 8.9. A mechanism with an air chamber coupling the diaphragm to the horn. The 

 variation in volume of the air chamber introduces a nonhnear element in the form of the 

 acoustic capacitance Cai- The equivalent electrical circuit indicates the effect of the non- 

 hnear element upon the system. The wave shapes of the electrical input and the acoustical 

 output for a low, high, and a combination of a high and a low frequency illustrates the 

 effect of the nonlinear element upon the acoustical output. 



of the diaphragm may be so large that the volume of the air chamber 

 becomes alternately zero and two times the normal volume, the acoustic 

 reactance of the acoustic capacitance is very small compared to the acoustic 

 resistance of the horn. See Fig. 8.9. At the high frequencies where the 

 acoustic reactance of the acoustic capacitance is comparable to the acoustic 

 resistance, the amplitude of the diaphragm for the same output is so small 

 that the variation in acoustic capacitance may be neglected. See Fig. 8.9. 

 However, the conditions are different when both a high and a low frequency 

 are impressed upon the same system. Under these conditions considerable 

 change in capacitance occurs due to the large amplitudes of the diaphragm 

 for the impressed low frequency. The resultant change in capacitance 

 introduces a variable element for the impressed high frequency which may 

 have variations in impedance as large as the impedance of the other ele- 

 ments of the system. The result is shown in Fig. 8.9. When this con- 



