268 BELL SYSTEM TECHNICAL JOURNAL 



was taken equal to 0.060 in. Figure 4 shows that aco^ has a minimum 

 value at about 50 cycles, where a is equal to about 0.4. These values 

 give a ratio of 4.5 for T. 



Inasmuch as i? = • , where a is the resistivity of the wire used 



for the coil and v the volume of the coil, from equation (3) is obtained 



Bh = naTholO\ (5) 



The first member gives the total magnetic energy that must be set 

 up in the region occupied by the driving coil. This value is fixed by 

 the fact that all factors in the second member are specified. The 

 same performance is obtained with a small coil and high flux density 

 as with a large coil and low flux density, provided B'^v is held fixed, 

 but the coil in any case should not be made so small that it will be 

 incapable of radiating the heat generated within it without danger of 

 overheating, nor so large that the mass reactance of the coil will 

 reduce the efficiency at the higher frequencies. 



This receiver unit, when constructed according to the above prin- 

 ciples and when connected to an amplifier and a horn in the specified 

 manner, should be capable of delivering power 3 or 4 times that de- 

 livered by the orchestra in the frequency region lying between 35 and 

 400 c.p.s., with an efficiency of about 70 per cent, and with a variation 

 in sound output for a given input power to the amplifier of not more 

 than 1 db throughout this range. 



The High Frequency Horn 



It is well known that a tapered horn of the ordinary type has a 

 directivity which varies with frequency. Sound of low frequency is 

 projected through a relatively large angle. As the frequency is 

 increased this angle decreases progressively until, at frequencies for 

 which the wave-length is small compared with the diameter of the 

 mouth opening, the sound beam is confined to a very narrow angle 

 about the axis of the horn. 



If we had a spherical source of sound (i.e., a source consisting of a 

 sphere, the surface of which has a radial vibratory motion equal in 

 phase and amplitude at every point of the surface), sound would be 

 radiated uniformly outward in all directions; or, if we had only a 

 portion of a spherical surface over which the motion is radial and 

 uniform, uniform sound radiation still would prevail throughout the 

 solid angle subtended at the center of curvature by this portion of the 

 sphere, provided its dimensions were large compared with the wave- 

 length. Throughout this region the sound would appear to originate 



