266 BELL SYSTEM TECHNICAL JOURNAL 



with a throat diameter of 8 inches is shown in Fig. 4. These curves were 

 computed under the assumption that the mouth of the horn is sur- 

 rounded by a plane baffle of infinite extent, a condition closely approx- 

 imated if the horn rests on a stage floor. 



Low Frequency Receiving Unit 

 When a moving coil receiving unit, coupled to a horn, is connected 

 to an amplifier having an output resistance equal to w — 1 times 

 the damped resistance R of the driving coil, it can easily be shown that 

 the sound power output is 



P = -F J„.„ ■ . ./„-,. watts, (2) 



^^ + ^ 



+ Ixa + T'xJ 



where E is the open circuit voltage of the amplifier, L the length of 

 wire in the receiver coil, T the ratio of the area of the diaphragm to 

 the throat area of the horn, r + jx the throat impedance of the horn, 

 and Xd the mechanical reactance of the diaphragm and coil, the 

 mechanical resistance of which is assumed to be negligibly small. 

 From Fig. 4 it may be seen that the mean value of x increases as the 

 frequency decreases to a value below 40 c.p.s., and that x is smaller 

 than r except at the very lowest frequencies. If, therefore, the stiffness 

 of the diaphragm be adjusted so that Xd is equal to T^ times the mean 

 value of X at 40 c.p.s., the second term in the denominator may be 

 neglected without much error because it will have but little effect 

 upon the sound output except at the higher frequencies, where the 

 mass reactance of the coil and diaphragm may have to be taken into 

 account. 



If minimum variations in sound output are desired for variations 

 in r, 



B^mo-^ _ ... 



where ro is equal to the geometric mean value of r, which is approx- 

 imately equal to Ape. 



If a is the ratio of the resistance at any frequency to the mean 

 value, and if the second term in the denominator is neglected, equation 

 (2) becomes 



P=^ ^. (4) 



In Fig. 4 it is shown that above 35 c.p.s. a has extreme values of 2.75 

 and 0.36, at which points there will be minimum values in P, but these 



