NONLINEAR DISTORTION 137 



velocity is not appreciably affected by the suspension because the reac- 

 tance of the compliance Cms is small compared to the impedance of the 

 remainder of the system. Below the resonance frequency the reactance of 

 the compliance is the controlling impedance. In this range the nonhnear 

 characteristics of the suspension will be most marked. The characteristics 

 of Fig. 7.15 show the total distortion for 2, 5 and 10 watts input to the loud 

 speaker. The distortion increases with input and with decrease of the 

 frequency. The fundamental resonance frequency of this loud speaker 

 occurred at 80 cycles. It will be seen that the distortion is very small 

 above the resonance frequency where the influence of the suspension com- 

 pliance is small. The distortion due to the suspension system may be 

 obviated by placing the fundamental resonance frequency of the loud 

 speaker at the lower limit of the reproduction range. 



Inhomogeneity of the flux density through which the voice coil moves 

 is another source of distortion. The result is that the driving force does 

 not correspond to the voltage developed by the generator in the electrical 

 driving system. Furthermore, the motional impedance is a function of 

 the amplitude. This type of distortion can be eliminated by making an 

 air gap of a sufficient axial length so that the voice coil remains at all times 

 in a uniform field. This type of distortion can also be eliminated by mak- 

 ing the voice coil longer than the air gap so that the summation of the 

 products of each turn and the flux density is a constant. See Sec. 8.3D. 



The distortions referred to above have been concerned with higher har- 

 monics, that is, multiples of the fundamental. It has been analytically 

 shown by Pederson ^^' ^^ that subharmonics are possible in certain vibra- 

 ting systems. The existence of subharmonics in direct radiator loud 

 speakers is quite well known. It has been noticed that, by impressing a 

 steady tone upon a system which produces both subharmonics and higher 

 harmonics, the subharmonics are more pronounced and objectionable to the 

 ear than the higher harmonics. However, by actual measurement under 

 these conditions the subharmonic was less than one per cent, while the 

 higher harmonics were several per cent of the fundamental. The ex- 

 planation appears to be that it is more difficult to mask a low tone with 

 a high tone than the reverse procedure. Another feature of subharmonic 

 phenomena is the relatively long time required for " build up." Con- 

 ventional sound reproduction does not usually require the reproduction 

 of a single isolated high frequency tone of long duration. For examples 

 of subharmonic distortion see Sec. 8.3£. 



I'' Pederson, P. O., Jour. Acous. Soc. Amer., Vol. 6, No. 4, p. 227, 1935. 

 11 Pederson, P. O., Jour. Acous. Soc. Amer., Vol. 7, No. 1, p. 64, 1936. 



