20 ACOUSTICAL RADIATING SYSTEMS 



The intensity or average power, in ergs per second, transmitted through 

 a unit area at a distance r, in centimeters, is the product of ^ and u and is 

 given by 



The total average power in ergs per second emitted by the source is 



Pt = lirpck^A^ 2.6 



where p = density of the medium, in grams per cubic centimeter, 

 c = velocity of sound, in centimeters per second, 

 k = 27r/X, 



X = wavelength, in centimeters, and 

 A is defined by equation 2.1. 



B. Point Source Radiating into a Semi-Infinite Medium. Solid Angle 

 of 2t Steradians. — The above example considered a point source operating 

 in an infinite medium. The next problem of interest is that of a point 

 source operating in a semi-infinite medium, for example, a point source 

 near an infinite wall. 



In this case we can employ the principle of images as shown in Fig. 2.1. 

 The pressure, assuming the same distance from the source, is two times 

 that of the infinite medium. The particle velocity is also two times that 

 of the infinite medium. The average power transmitted through a unit 

 area is four times that of the infinite medium. The average power out- 

 put of the source, however, is two times that of a simple source operating 

 in an infinite medium. 



C. Point Source Radiating into a Solid Angle of t Steradians. — Em- 

 ploying the method of images Fig. 2.1 the pressure is four times, the par- 

 ticle velocity is four times and the average power transmitted through a 

 unit area is sixteen times that of an infinite medium for the same distance. 

 The average power output of the source is four times that of a simple 

 source operating in an infinite medium. 



D. Point Source Radiating into a Solid Angle of -wjl Steradians . — Em- 

 ploying the method of images. Fig. 2.1, the pressure is eight times, the 

 particle velocity eight times and the average power transmitted through a 

 unit area is sixty-four times that of the same source operating in an infinite 

 medium at the same distance. The average power output is eight times 

 that of the same simple source operating in an infinite medium. 



E. Application of the Simple Source. ■ — ■ The above data may be applied 

 to acoustic radiators in which the dimensions are small compared to the 



