CURVED SURFACE SOURCE 



35 



blance to those of an arc of the same angular spread. For example, the 

 angular spread of the horn of Fig. 2.11 in the plane containing the line 

 AA' and the axis is 87|°. This may be compared to the arc of Fig. 2.5. 

 In this case X '4, X 2, X, 2X, 4X and 8X will correspond to 145, 290, 580, 

 1160, 2320 and 4640 cycles. The angular spread in the plane containing 

 the line BB' and the axis is 52|°. This may be compared to the 60° arc 



aso'v 



lOOO/v 



Fig. 2.13. Directional characteristics of the 15-cell cellular horn shown in Fig. l.WA in a 

 plane containing the line A-A' and the axis of the center horn. The polar graph depicts the 

 pressure, at a fixed distance, as a function of the angle. The pressure for the angle 0° is 

 arbitrarily chosen. 



of Fig. 2.4 with the same relation between the wavelengths and frequencies 

 as noted above. It will be seen that there is a marked resemblance be- 

 tween corresponding frequencies. Of course, there is some variation due 

 to the fact that the frequencies do not correspond exactly. Further, 

 there is some difference in the angular spread. For most spherical sur- 

 faces of this t)^e the directional characteristics in various planes corre- 

 spond very closely to the directional characteristics of the corresponding arc. 



Directional systems are used for sound ranging both in air and in water. For 

 the general subject of sound ranging and signaling, see Stewart and Lindsay, 

 " Acoustics," D. Van Nostrand Company, New York City, and Olson and Massa, 

 " Applied Acoustics," Blakiston Company, Philadelphia. 



Equations, 2.23 and 2.25 are applicable to plane and curved acoustic diffraction 

 gratings. As in the case of optics the angle of the maxima shifts with the frequency. 

 Gratings have been used in systems for the analysis of sound. The audio fre- 

 quency is used to modulate a high frequency oscillator (50,000 cycles). The output 

 of the oscillator drives a high frequency loud speaker which illuminates the grating 

 with the high frequency sound. The sound diffracted from the grating is spread 

 out in a spectrum corresponding to the original audio frequency sound. The sound 

 in this spectrum is picked up by a small microphone, amplified, detected and fed 

 to a suitable indicator. See Mever, E., Jour. Acous. Soc. Anier., Vol. 7, No. 5, 

 p. 88, 1935. 



