ACOUSTIC IMPEDANCE. 31 



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

 conductor, and the simultaneous alternating current I in the element 



aE = - I (i^co) dl rms. volts Z (31) 



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

 and the linear resistance r of the conductor is ignored. Here co 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 



dF , d-x dynes , , 



— — - = mv- T^ ,; Z (4^) 



dl oh Imear cm. 



dx 

 Integrating F = — my- — + constant dynes Z (33) 



ol 



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



the pressure deviation from the normal pressure F^ over a cross-section 



dx s 



of the tube, vanishes when tt = 0. 



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



Differentiating with respect to time: 



^F m ^ ni " 1 • cm.-dynes , . 



— 51 = F 51 = — mr dx Z (35) 



dt sec. 



or 



cm.-dvnes , , 



jcoFdl= - rnv'^dx ^ Z (36) 



and 



dx = - "^'^^Fai rms. kinesZ (37) 



The quantity mv^ may be replaced by S, the total elastic force resisting 

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

 tion; so that the instantaneous differential increase in A-ibrational 

 velocity over an element of length d\ is • 



dx = -F Ij^j dl rms. kinesZ (38) 



The quantity s is the normal adiabatic elastic force Spo —Syp^, of the 

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



