264 BELL SYSTEM TECHNICAL JOURNAL 



latter was used in the Philadelphia-Washington experiment because 

 it appears to have definite advantages where such large amounts of 

 power are to be radiated. The horn type can be given the desired 

 directive properties more readily, and higher values of efficiency 

 throughout, a wide frequency range are more easily realized. In 

 consideration of the large power requirements, high efficiency is of 

 special importance because it will keep to the lowest possible value the 

 power capacity requirements of the amplifiers and because, with the 

 heating proportional to one minus the efficiency, the danger of burning 

 out the receiving units is reduced. 



For efficiently radiating frequencies as low as 40 c.p.s., a horn of large 

 dimensions is required. In order that the apparatus may not become 

 too unwieldly the folded type of horn is preferable, but a large folded 

 horn transmits high frequency tones very inefficiently. As actually 

 used, therefore, the loud speaker was constructed in two units: one for 

 the lower and the other for the higher frequencies, an electrical network 

 being used to divide the current into two frequency bands, the point 

 of division being about 300 c.p.s. 



The Low Frequency Horn 

 When moderate amounts of power are transmitted through a horn 

 the sound waves will suffer very little distortion, but when the power 

 per unit area becomes large, second-order effects, usually neglected in 

 considering waves of small amplitude, must be taken into account. 

 The transmission of waves of large amplitude through an exponential 

 horn has been investigated theoretically by M. Y. Rocard.^ His 

 investigation shows that if W watts are transmitted through the 

 throat of an exponential horn a second harmonic of intensity RW will 

 be generated, where R is given by the relation 



(7 + \)T X WW 



2pc\fM • ^^ 



in which/ is the frequency of the fundamental, /o the cut-off frequency 

 of the horn, c the velocity of sound, p the density of air, and A the 

 area of the throat of the horn, all expressed in c.g.s. units. It may 

 be noted that the intensity of the harmonic increases with the ratio 

 of the frequency to the cut-off frequency of the horn; this is another 

 argument against attempting to cover too wide a range of frequencies 

 with a single horn. In Fig. 1 it is shown that in the region of 200 

 c.p.s. the orchestra gives peak powers of about 10 watts. If, therefore, 

 30 watts be set as the limit of power that the horn is to deliver at 200 

 c.p.s., 32 c.p.s. as the cut-off frequency of the horn, and 30 db below 



