54 



ANALOGIES 



Acous- 

 These 



in the acoustical system is represented as the fluid contained in a tube in 

 which all the particles move with the same phase when actuated by a force 

 due to pressure. These elements are analogous to inductance in the 

 electrical system. 



Compliance in the mechanical system is represented as a spring, 

 tic capacitance is represented as a volume which acts as a stiffness 

 elements are analogous to capacitance in the electrical system. 



4.6. Electrical, Mechanical and Acoustical Systems of One Degree of 

 Freedom. — In the preceding sections the fundamental elements in each 

 of the three systems have been defined. From these definitions it is evi- 

 dent that friction, mass and compliance govern the movements of physical 

 bodies in the same manner that resistance, inductance and capacitance 

 govern the movement of electricity. In any dynamical system there are 



e c^: 



m 



/77777m77m7f77777 



P li M C^ 



ELECTRICAL 



MECHANICAL 



ACOUSTICAL 



Fig. 4.2. Electrical, mechanical and acoustical systems of one degree of freedom. (Courtesy 

 of The Blakiston Company from Olson and Massa, " Applied Acoustics.") 



two distinct problems, namely: the derivation of the differential equations 

 from the statement of the problem, and the physical laws and the solution 

 of the differential equation. Mathematically the elements in the electrical 

 circuit are the coefficients in the differential equation. In the same way 

 the coefficients in the differential equations of a mechanical or acoustical 

 system may be looked upon as mechanical or acoustical elements. It is 

 the purpose of this section to describe the action of electrical and acous- 

 tical systems from this viewpoint. An electrical, mechanical and acoustical 

 system of one degree of freedom is shown in Fig. 4.2. In one degree of 

 freedom the activity in every element of the system may be expressed in 

 terms of one variable. In the electrical system an inductance Z-, a re- 

 sistance Te-, a capacitance Ce and an electromotive force e are connected in 

 series. In the mechanical system, a driving force /m acts upon a particle 

 of mass m fastened to a spring Cm and sliding upon a plate with a frictional 

 force which is proportional to the velocity and designated as Vm- In the 

 acoustical system, an impinging sound wave of pressure p acts upon an 



