148 BELL SYSTEM TECHNICAL JOURNAL 



(pressure)^ 

 is equal to t-t-ij ergs per second, and the power input. The 



operating efficiency is the ratio of these two quantities. The dots 

 plotted in Fig. 7 give the values of the efficiencies so obtained. These 

 values are seen to agree closely with those calculated from the motional 

 impedance. This agreement shows that the mechanical power losses 

 in the receiver are small. 



Curve A in Fig. 7 gives the efficiency as calculated from the con- 

 stants of the receiver by means of the formula given in appendix B, 

 under the assumption that the mechanical impedance imposed on the 

 diaphragm and the air chamber has the same value throughout the 

 whole frequency range, viz., 16.7 A' c.g.s. units, where A is the effective 

 area of the diaphragm. It is seen that the calculated and measured 

 values are in good agreement except for certain irregularities at the 

 higher frequencies. Whether these irregularities are to be ascribed to 

 the action of the air chamber or to a change in the mode of motion of 

 the diaphragm we are not at present prepared to say. 



The curves of Fig. 7 give an efficiency for this receiver of about 50 

 per cent over a wide frequency range. This efficiency is within 3 T.U. 

 of the possible maximum of 100 per cent. We may remark at this 

 point that it is conceivably possible to build a receiver which will 

 sound louder than one having an efficiency of 100 per cent. If, for 

 instance, a receiver introduces harmonics on account of amplitude 

 distortion, a low frequency driving force may give rise to a tone of 

 higher frequency, where the ear may have a sensitivity many times 

 greater than at the driving frequency. An increase in loudness ob- 

 tained in this way of course exacts a sacrifice in the faithfulness of 

 reproduction. The difference in loudness between the sound emitted 

 by this receiver and by ordinary commercial types of loud speakers, 

 for the same power input, is considerable, since most of them have an 

 efficiency of less than one per cent for speech frequencies. Not only 

 does this receiver have a high efficiency over a wide frequency range 

 but it is free from any sharp variations in efficiency with frequency, a 

 condition of great importance in the quality of reproduction. 



A mplitude Distortion 

 Thus far we have discussed only the frequency characteristic of the 

 receiver. There still remains to be considered the proportion of 

 harmonics that are generated by the receiver when supplied with a 

 current of sine wave form. These harmonics are generated when the 

 displacement of the diaphragm is not proportional to the input current. 

 At low frequencies the amplitude of motion for a given power output 



