CHAPTER II 

 ACOUSTICAL RADIATING SYSTEMS 



2.1. Introduction. — There are almost an infinite number of different types 

 of sound sources. The most common of these are the human voice, musi- 

 cal instruments, machinery noises and loud speakers. The most impor- 

 tant factors which characterize a sound source are the directional pattern, 

 the radiation efficiency and the output as a function of the frequency. 

 In the case of some sound sources as, for example, musical instruments, 

 it is almost impossible to analyze the action. However, in the case of 

 most sound reproducers the action may be predicted with amazing 

 accuracy. It is the purpose of this chapter to consider some of the simple 

 sound sources that are applicable to the problems of sound reproduction, 



2.2. Simple Point Source. — A point source is a small source which 

 alternately injects fluid into a medium and withdraws it. 



A, Point Source Radiating into an Infinite Medium. Solid Angle of 

 47r Steradians . — Consider a point source having a maximum rate of fluid 

 emission of ^-kA cubic centimeters per second. The momentary rate at 

 a time / is ^-kA cos co/. The maximum rate of fluid emission may be 

 written 



-^-kA = ^lo 2.1 



where S = area of the surface of the source, in square centimeters, and 



^0 = maximum velocity, in centimeters per second over the sur- 

 face S. 

 The velocity potential of a point source from equation 1.36 is 



0^ = - ^inct-r) 2.2 



r 



The particle velocity at a distance r from equation 1.42 is 



u = — cos k{ct — r) — sin k{ct — r) 2.3 



r \_kr J 



The pressure at a distance r from equation 1.40 is 



pkcA ... , 



p = sm k [ct — r) 2.4 



r 



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