IMPEDANCE CONCEPT AND APPLICATION 23 



pedance" will be used to designate a constant of the medium without 

 reference to any particular wave. 



Vibrating Strings 



In strings under constant tension r, simply periodic waves may be 

 described by the following two equations : 



dF / , • N dv iw ^ 



-T— = — [r -\- tcomjv, -T- = r, 



ax ax T 



where m is the mass and r the resistance per unit length of the string. 

 The variable F represents the force on a typical point of the string at 

 right angles to the string and v is the velocity at that point. 



Hence the characteristic impedance and the propagation constant 

 are given by 



Zo = J- -. , r = y^ (r -]- lo^m) — . 



In the non-dissipative case we have simply 



-7 I T • /^ 



Zo = ymr, 1 = tu) \ — . 



Heat Waves 



Transmission of heat waves is also a special case of the generalized 

 transmission line theory. In the one-dimensional case we have 



dT _ V dv _ _ dT 



'dx~ ~K' dx~ ~ ^ 'dt' 



where : T is the temperature, v the rate of heat flow, K the thermal 

 conductivity, 8 the density and c the specific heat. For simply peri- 

 odic waves, we obtain 



dT 1 dv . . „ ■ 



-— =-— y, — =- to}c8 I . 

 dx K dx 



Thus the characteristic impedance and the propagation constant of 

 heat waves are 



1 _ \i(acb 



Zo = 



The ratio "the temperature of the source/the rate of heat flow from 

 the source" is the impedance "seen" by the heat source. 



