CHAPTER IV 

 ELECTRICAL, MECHANICAL AND ACOUSTICAL ANALOGIES 



4.1. Introduction. — Systems in use to-day for sound reproduction in- 

 clude mechanical, acoustical, electro-acoustical, electro-mechanical, me- 

 chano-acoustical and electro-mechano-acoustical systems. Almost any 

 work involving mechanical or acoustical systems also includes electrical 

 systems and electric circuit theory. Acoustical measurements are usually 

 made with electrical instruments and in terms of electrical quantities. 

 Ultimately the electrical units must be compared with acoustical and me- 

 chanical units. In general, anyone in any manner connected with sound 

 reproduction must be familiar with electric circuit theory. Therefore, it 

 is logical, whenever possible and convenient, to treat mechanical and 

 acoustical problems by the same mathematical theory as is used in electric 

 circuit problems. 



Electric circuit theory is the branch of electromagnetic theory which 

 deals with electrical oscillations in linear electrical networks. An elec- 

 trical network is a connected set of separate circuits termed branches or 

 meshes. These branches or meshes are composed of elements. Resis- 

 tance, inductance and capacitance are termed elements. 



Mathematically the elements in an electrical circuit are the coefficients 

 in the differential equations. The equations of electric circuit theory may 

 be based upon Maxwell's dynamical theory. In this case the network 

 forms a dynamical system in which the currents play the role of velocities. 

 In the same way the coefficients in the differential equations of a mechani- 

 cal or acoustical system may be looked upon as mechanical or acoustical 

 elements. In other words, every electrical, mechanical or acoustical sys- 

 tem may be considered as a combination of electrical, mechanical or 

 acoustical elements. Therefore, any mechanical or acoustical system may 

 be reduced to an electrical network. Then the problem may be solved by 

 electric circuit theory. 



It is the purpose of this chapter to consider electrical, mechanical and 

 acoustical elements and the combination of elements and to indicate analo- 

 gies between the elements and connections in the three systems. 



4.2. Resistance. — A. Electrical Resistance. — Resistance is the circuit 

 element which causes dissipation. 



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