PLANE CIRCULAR SURFACE SOURCE 



29 



OrAMETER- J 



DIAMETER. fX 



DIAMETER -X 



DIAMETER "I5X DIAMETER-3X 



Fig. 2.7. Directional characteristics of a circular line or ring source as a function of the 

 diameter and wavelength. The polar graph depicts the pressure, at a large fixed distance, 

 as a function of the angle. The pressure for the angle 0° is arbitrarily chosen as unity. The 

 direction corresponding to the angle 0° is the axis. The axis is the center line perpendicular 

 to the plane of the circle. The directional characteristics in three dimensions are surfaces 

 of revolution about the axis. 



2.7. Plane Circular Surface Source. — The directional characteris- 

 tics ^^' ^^ of a circular surface source with all parts of the surface vibrating 

 with the same intensity and phase is 



2/1 ( — — sin (X 

 Ra = — -^-^ '- 2.28 



IttR 



sin a 



where Ra = ratio of the pressure for an angle a to the pressure for an 

 angle a — 0, 

 /i = Bessel Function of the first order, 

 R = radius of the circle, in centimeters, 

 a = angle between the axis of the circle and the line joining the 



point of observation and the center of the circle, and 



X = wavelength, in centimeters. 



The directional characteristics of a plane circular surface source as a 



function of the diameter and wavelength are shown in Fig. 2.8. The 



characteristic is somewhat broader than that of the uniform line of length 



equal to the diameter of the circle, but has approximately the same form. 



Equation 2.28 for the directional characteristics of a circular surface 



" Stenzel, H., Ekk. Nach. Tech., Vol. 4, No. 6, p. 1, 1927. 



12 Wolff, L and Maker, L., Jour. Acous. Soc. Amer., Vol. 2, No. 2, p. 201, 1930. 



