34 



ACOUSTICAL RADIATING SYSTEMS 



where d = the distance between the center of the mouth of the horn and 

 the reference plane X'O'Z', in centimeters, and 

 X = wavelength, in centimeters. 

 The vectors, having amplitudes Ji, Ai, Az, A^, etc., determined from the 

 directional characteristics and having phase angles ^i, d^, 6s, Oa, etc., 

 determined from equation 2.29, are added vectorially as shown in Fig. 2.115. 

 This method of predicting the directional characteristics assumes that 

 there is no interaction between individual horns which changes the com- 

 plexion of the velocities at the mouth from that which obtains when 

 operating an individual horn. Obviously, this condition is not absolutely 

 satisfied. Apparently, the discrepancy has no practical significance be- 



250^ 



500<v 



lOOO'V 



Fig. 2.12, Directional characteristics of the 15-cell cellular horn shown in Fig. 2.11yf in 

 a plane containing the line B-B' 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. 



cause it has been found that this method of analysis agrees quite well with 

 experimental results. 



The directional characteristics of the cellular horn of Fig. l.WA are 

 shown in Figs. 2.12 and 2.13. Above 2000 cycles the dimensions of the 

 total mouth surface are several wavelengths and the directional character- 

 istics are fairly uniform and defined by the total angular spread. Where 

 the dimensions are comparable to the wavelength the directional char- 

 acteristics become very sharp, as shown by the polar curves for 500 and 

 1000 cycles. Then, as the dimensions of the surface become smaller than 

 the wavelength, 250 cycles, the angular spread broadens, as is illustrated 

 by the larger spread for the smaller vertical dimension when compared to 

 the smaller spread for the larger horizontal dimension. 



The directional characteristics of a cellular horn show a striking resem- 



