CURVED LINE SOURCE 



25 



n — number of sources, 



d = distances between the sources, in centimeters, and 

 X = wavelength, in centimeters. 

 If the number of sources n approach infinity and d, the distance between 

 the sources, approach zero in such a way that 



nd = I 



the hmiting case is the hne source. If this is carried out equation 2.23 

 becomes 



Ra — 



. it/ . 

 sm — sm a 

 X 



T. 



2.24 



sm a 



The directional characteristics of a continuous line source are shown in 

 Fig. 2.3. The directional characteristics are symmetrical about the line 

 as an axis. Referring to Fig. 2.3, it will be seen that there is practically 



LENGTH .# 



LENGTH -3X 



Fig. 2.3. • Directional characteristics of a line source as a function of the length and the wave- 

 length. 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 corre- 

 sponding to the angle 0° is perpendicular to the line. The directional characteristics in 

 three dimensions are surfaces of revolution about the line as an axis. 



no directivity when the length of the line is small compared to the wave- 

 length. On the other hand, the directional characteristics are sharp when 

 the length of the line is several wavelengths. 



2.5. Curved Line Source (Arc of a Circle). — A curved line source may be 

 made up of a large number of points on the arc of a circle separated by 

 very small distances. The directional characteristics of such a line in the 



