32 



ACOUSTICAL RADIATING SYSTEMS 



piston which will yield the same directional characteristic is smaller than 

 the mouth. These results also show that the directional characteristics 

 vary very slowly with frequency at these smaller wavelengths. Referring 

 to Fig. 2.10, it will be seen that for any particular high frequency, 4000, 

 7000 or 10,000 cycles per second, the directional characteristics become 

 progressively sharper as the rate of flare decreases. 



The results of Figs. 2.9 and 2.10 are appHcable to other geometrically 

 similar horns by changing the wavelength (or the reciprocal of the fre- 

 quency) in the same ratio as the linear dimensions. 



2000 '\< 4000ro 7000 'V 10000 ro 



Fig. 2.10. The directional characteristics of a group of exponential horns, with a mouth 

 diameter of 12 inches and a throat diameter of f inches, as a function of the flare. The 

 number at the right of each polar diagram indicates the diameter of a circular piston which 

 will yield the same directional characteristic 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 

 as unity. The direction corresponding to 0° is the axis of the horn. The directional 

 characteristics in three dimensions are surfaces of revolution about the horn axis. 



2.9. Curved Surface Source. — A sphere vibrating radially radiates 

 sound uniformly outward in all directions. A portion of a spherical surface, 

 large compared to the wavelength and vibrating radially, emits uniform 

 sound radiation over a solid angle subtended by the surface at the center 

 of curvature. To obtain uniform sound distribution over a certain solid 

 angle, the radial air motion must have the same phase and amplitude over 

 the spherical surface intercepted by the angle having its center of curvature 

 at the vertex and the dimensions of the surface must be large compared 



