26 



ACOUSTICAL RADIATING SYSTEMS 



plane of the arc is, 



Rn, = 



1 



2m + 1 



k = m 



^ COS 



k=—m 



[^ 



COS {a + kd) 



2.25 



. *="^ . r27ri? ^ , ■ 



-\- J Z^ sin cos (a + ^0) 



k=—m L ^ J I 



where jRq, = ratio of the pressure for an angle a to the pressure for 



an angle a = 0, 

 a. = angle between the radius drawn through the central 

 point and the line joining the source and the distant 

 observation point, 

 X = wavelength, in centimeters, 

 R = radius of the arc, in centimeters, 

 2w + 1 = number of points, 



Q = angle subtended by any two points at the center of the 



arc, and 

 k = variable. 

 Another method ^ is to break up the arc into a large number of equal 

 chords. The intensity is assumed to be uniform over each chord. Also the 

 phase of all of the chords is the same. In this case the result takes the form, 



Ra = 



1 



2;;2 + 1 



IttR 



sm 



Z^ cos j — 



k=—m I A 



cos (a + kd) 



X 



sin {a + kd) 



vd 



sin {a + kd) 



+ J 2- sm \—^ — cos {a + kd) 



sm 



sin (a + kd) 



k = —m 



— sm (a + kd) 



2.26 



^here 



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

 an angle a = 0, 

 X = wavelength, in centimeters, 

 k = variable, 



R = radius of the arc, in centimeters, 

 2m + 1 = number of chords, 



d = angle subtended by any of the chords at the center of 



circumscribing circle, and 

 d = length of one of the chords, in centimeters. 



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



