NONLINEAR DISTORTION 157 



and negative changes in pressure are impressed upon a mass of air the 

 resultant changes in volume will not be the same. The volume change for 

 an increase in pressure will be less than the volume change for an equal 

 decrease in pressure. From a physical viewpoint the distortion may be 

 said to be due to the nonlinearity of the air. 



In the derivation of the fundamental wave equation the second order 

 terms were omitted. If these terms are included the magnitude of the 

 harmonic frequencies may be determined from the differential equation. 

 The subject has been investigated both theoretically and experimentally 

 by a number of investigators. In the case of an exponential horn for 

 constant sound power output, the distortion is proportional to the 

 frequency. Further, the nearer the observation frequency is. to the 

 cutoff frequency the smaller the distortion. 



The distortion due to nonlinearity of the air is at the present time one 

 of the most important as well as the most troublesome factors in the design 

 of high efficiency loud speakers for large outputs. In order to obtain high 

 efficiency, particularly at the higher frequencies, it is necessary to couple 

 the relatively heavy diaphragm to a throat small in area compared to the 

 diaphragm. For a certain allowable distortion the power output is directly 

 proportional to the area of the throat. Obviously, to deliver large sound 

 outputs with small distortion requires a very large throat which may be 

 suitably coupled to a correspondingly large diaphragm or a large number of 

 lightly driven small throat units. 



The power ^^ which can be transmitted per square centimeter of throat 

 area of an iniinite exponential horn as a function of the ratio of the fre- 

 quency under consideration to the cutoff frequency with the production 

 of 1, 3 and 10 per cent distortion is shown in Fig. 8.8. For the sake of 

 generality the curves shown in Fig. 8.8 refer to an infinite horn. How- 

 ever, the increase in power which may be transmitted by a practical finite 

 horn is only a few per cent greater than that shown in Fig. 8.8, because 

 very little distortion is generated in the large cross-sectional area near the 

 mouth of the horn. 



It may be mentioned in passing that the multiple flare horn (see Sec. 5.23) 

 provides a means of decreasing the distortion because the rate of flare is 

 very rapid near the diaphragm and, therefore, the pressures are rapidly 

 reduced with respect to the distance from the diaphragm. 



B. Distortion Due to Variation in Volume of Air Chamber'^^.— In general, 

 acoustical, mechanical and electrical networks are assumed to be invariable; 



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



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



