150 BELL SYSTEM TECHNICAL JOURNAL 



tone. If a horn were connected to the receiver in place of the tube, in 

 addition to the resistance, a mass reactance would generally be imposed 

 on the diaphragm at the lower frequencies. Under these conditions 

 the proportion of harmonics introduced would be still lower than that 

 indicated in Fig. 9. 



At the higher frequencies the power output is limited solely by the 

 current-carrying capacity of the coil. At these frequencies the steady 

 power input for a temperature rise of 100 degrees C. is about 30 watts. 

 With an efficiency of 50 per cent the corresponding output would be 

 15 watts. 



After the work described in this paper was for the most part done 

 and as a result of the extremely promising performance of the first 

 models, a design of the receiver built along essentially these lines was 

 worked into a form suitable for commercial production by Mr. W. C. 

 Jones and Mr. L. W. Giles. These receivers are now in commercial 

 use in Vitaphone and Movietone installations. As commercially pro- 

 duced in quantities numbering several thousand, efficiencies of the 

 order of 30 per cent have been realized. 



In conclusion, we wish to express our appreciation for the valuable 

 assistance given by Mr. T. F. Osmer in carrying out most of the 

 experimental work described in this paper. 



Appendix A 



Consider a diaphragm and connecting air chamber of the form shown 

 in Fig. 1 . Assume that the air chamber is of a form such that the cross- 

 sectional area at any distance r from the center is equal to the throat 

 areaof the horn, i.e., 27rr/ = -irr^-. This form of connecting air chamber 

 then differs but little from that used in most commercial types of horn 

 speakers. The sound output is in general dependent on the mode of 

 motion of the diaphragm. In most loud speakers this mode of motion 

 varies with the frequency. However, let us assume that we have a 

 paraboloidal displacement at all frequencies. The velocity at any 

 radial distance may then be represented by 



^ 



'-'s 



■],.. 



if ^0^'"' is the velocity at the center. 



Under the assumed conditions, the sound transmitted through the 

 throat is very nearly the same as that which would be transmitted 

 along the positive direction through the tube sketched in Fig. 10, which 

 extends to infinity in both directions, provided the portion of the wall 



