CHAPTER V 

 ACOUSTICAL ELEMENTS 



5.1. Introduction. The preceding chapter is devoted to analogies be- 

 tween electrical, mechanical and acoustical systems. The purpose of draw- 

 ing these analogies is to facilitate the solution of problems in mechanical 

 and acoustical vibrating systems by converting these problems into the 

 corresponding electrical equivalents and solving the resultant electrical 

 circuits by conventional electrical circuit theory. An electrical circuit is 

 composed of electrical elements. In the same way the acoustical system 

 is composed of acoustical elements. The type of elements, that is, resis- 

 tance, inertance or capacitance, will depend upon the characteristic man- 

 ner in which the medium behaves for different sources of sound and in the 

 different ways of confining the medium. It is the purpose of this chapter 

 to consider acoustic elements and combination of elements. 



5.2. Acoustic Resistance. Acoustic resistance may be obtained by forc- 

 ing air through a small hole. The resistance is due to viscosity which may 

 be considered as friction between adjacent layers of air. In the ordinary 

 transmission of sound in a large tube the motion of all the particles in a 

 plane normal to the axis is the same, therefore the frictional losses are 

 small. When sound travels in a small tube the particle velocity varies 

 from zero at the boundary to a maximum at the center. The same is true 

 when a steady stream of air is forced through a small hole or tube, the 

 velocity of adjacent layers varies from zero at the boundary to a maximum 

 at the center. The smaller the hole the higher will be the resistance be- 

 cause of the greater effect of the sides. 



A small tube also has inertance. Therefore, the reactive component 

 increases with frequency. The mass reactance increases as the size of the 

 hole decreases as does the resistance, but at a slower rate. Therefore, the 

 mass reactance may be made negligible compared to the resistance if the 

 hole is made sufficiently small. 



Acoustic resistance employing viscosity may be made in various forms 

 as, for example, a large number of small holes or a large number of slits. 

 The acoustic impedance of fine holes and slits will be considered in the 

 next two sections. 



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