ACOUSTIC IMPEDANCE. 31 



electric pressure of emf. 5E, across an elementary length dl of a line 

 conductor, and the simultaneous alternating current I in the element 



dE = -I (j^^w) dl rms. volts Z (in) 



where 2 is the linear inductance of the conductor in henrys per km., 

 and the linear resistance r of the conductor is ignored. Here a; is the 

 angular velocity of the impressed electric pressure, and / is the length 

 of line in km., measured outwards from the generating end. 

 Again, from (27) and (29), we have • 



^F , d-.v dynes 



- — = m()2 — ^. -^ Z (32) 



oi dr hnear cm. 



r) )■ 



Integrating F = — mr „" + constant dynes Z (33) 



The constant of integration \'anishes, and may be dropped, because F 



the pressure dcA'iation from the normal pressure F^ over a cross-section 



dx 

 of the tube, vanishes when — = 0. 



dl 



Hence, F 51 = — lav" dx cm.-dynes Z (34) 



Differentiating with respect to time: 



dF 



— 61 = F ai = - mv- dx 



dt 



or 



./CO F 51 = — mi^ dx 



and 



dx = - • „ Fai 



my- 



The quantity mv- may be replaced by s, the total elastic force resisting 

 compression, expressed in ergs per cm. of displacement oA-er the sec- 

 tion; so that the instantaneous differential increase in A'il)rational 

 velocity over an element of length 51 is 



d.i- = -F Ij"^] dl rms. kines Z (38) 



The quantity s is the normal adiabatic elastic force S^o =Syp^, of the 

 medium over the section, 7 being the ratio of specific heats, and Po 



