LOUD SPEAKERS AND MICROPHONES 267 



minimum values will not lie more than 1 db below the maximum 



values. Hence, if the receiver satisfies the condition of equation (3), 



the extreme variations in the sound output will not exceed 1 db, 



although the horn resistance varies by a factor of 7.5. Also it may 



be stated here that when the condition of equation (3) is satisfied the 



horn is terminated at the throat end by a resistance equal to the surge 



resistance of the horn. Thus equation (3) establishes a condition of 



minimum values in the transient oscillations of the horn. 



B'^U X 10~^ 



The mean motional impedance of the loud speaker is tp^ , 



-TVo 



which, from equation (3), is equal to nR. The condition of equation 



(3) therefore specifies that the efiiciency of the loud speaker shall be 



ft 



— ; — 7 • The maximum power that an amplifier can deliver without 

 n -\- \ 



introducing harmonics exceeding a specified value is a function of the 



impedance into which it operates. Therefore, to obtain the maximum 



acoustic power for a specified harmonic content, the load impedance 



should have the value for which the product of the loud speaker 



efficiency and the power capacity of the amplifier has a maximum 



value. This optimum value of load impedance for the amplifier and 



loud speaker used in the Philadelphia-Washington experiments was 



found to be about 2.25 times the output impedance of the amplifier; 



the corresponding value of n then is 2.6 and the required efficiency 



72 per cent. For best operating condition a definite value of receiver 



efficiency thus is specified. 



The receiver may be made to satisfy the foregoing conditions 

 regardless of the value of T, the ratio of diaphragm area to throat area. 

 The area of the diaphragm has, however, a definite relation to the 

 maximum power that the receiver can deliver at the low frequencies. 

 The peak power delivered by the receiver is equal to T^aro^^u^ X 10~^ 

 peak watts where | is the maximum amplitude of motion of the 

 diaphragm. Figure 1 shows that in the region lying between 40 and 

 60 c.p.s., peak powers reach a value of from 1 to 2 watts. However, 

 the low frequency tones of an orchestra are undesirably weak and 

 may advantageously be reproduced at a relatively higher level. 

 Therefore it was decided to construct the loud speaker to be able to 

 deliver 25 watts in this region. 



As the coil moves out of its normal position in the air gap, the force 

 factor varies. Harmonics thus will be generated, the intensities of 

 which increase with increasing amplitude. A limit to the maximum 

 value of the amplitude ^ thus is set by the harmonic distortion that 

 one is willing to tolerate. In this receiver the maximum value of ^ 



