LOUD SPEAKERS AND MICROPHONES 271 



The High Frequency Receiving Unit 



In the design of the low frequency receiver one of the main objectives 

 was to reduce to a minimum the variations in sound transmission 

 resulting from variations in the throat impedance of the horn. How- 

 ever, the high frequency horn readily can be made of a size such that 

 the throat resistance has relatively small variations within the trans- 

 mitting region. On the other hand, whereas the diameter of the 

 diaphragm of the low frequency unit is only a small fraction of the 

 wave-length, that of the high frequency unit must be several wave- 

 lengths at the higher frequencies in order to be capable of generating 

 the desired amount of sound. Unless special provisions are made there 

 will be a loss in efficiency because of differences in phase of the sound 

 passing to the horn from various parts of the diaphragm. The high 

 frequency receiver therefore was constructed so that the sound gener- 

 ated by the diaphragm passes through several annular channels. 

 There are enough of these channels to make the distance from any 

 part of the diaphragm to the nearest channel a small fraction of a 

 wave-length. These channels are so proportional that the sound 

 waves coming through them have an amplitude and phase relation 

 such that a substantially plane wave is formed at the throat of the 

 horn. 



In the appendix it is shown that, for the higher frequencies where 

 the impedance of the horn may be taken as equal to pc times the 

 throat area and for the type of structure adopted, the radiation 

 resistance is equal to 



' ] 



pcaV^ 

 and the reactance 



. pea „ 



kVi^T^ + kH^ cot2 kl 



I 



fiT V 

 kl cot kl + ( -J- ) kl tan kl 



(6) 



(7) 



where a is the area of the throat of the horn, T the ratio of the area of 

 the diaphragm to the throat area, k =^ w/c, and the other designations 

 are those indicated in Fig. 11. At the lower frequencies the resistance 

 is Th and the reactance T^x, where r and x are, respectively, the 

 resistance and reactance of the throat of the horn. 



Equation 6 shows that at a given frequency, other conditions 

 remaining the same, the radiation resistance will have a maximum 

 value when / is approximately equal to ir/2k = c/4/. In Fig. 6 the 

 resistances as computed from equation (6) are plotted as a function 



