PHONOGRAPHS 237 



motion of the needle is transferred to the armature. The steady flux is 

 furnished by a permanent magnet. The armature is of the balanced type 

 so that in its central position there is no flux through the armature. When 

 the armature is deflected, a flux flows through the armature which induces 

 a voltage in the coil. Assume that the armature is deflected a distance 

 Ax. The flux, in maxwells, through the path 1, 2, assuming all the reluc- 

 tance resides in the air gap, is 



012 = ;r. 7-T 10.4 



2{a — Ax) 



where M = magnetomotive force of the magnet. In gilberts, 



a = spacing between the armature and the pole, in centimeters, and 

 Ax = deflection from the central position, in centimeters. 

 The flux through the path 2, 3 under these conditions is 



M 



*^23 = w} — — T^ 10.5 



Z{a -{- Ax) 



The flux, in maxwells, through the armature is 



MAx MAx 



If the displacement Ax takes place in the time A/, then the rate of change 

 of flux with respect to time, is 



A^^MAx^ 10 7 



At d^ At 



In the limit 



d4> M dx M ,^„ 



— = ■ — — = —-X 10.8 



dt a^ dt a^ 



The voltage in abvolts, generated in the coil is 



e = N —- = — —X 10.9 



dt a^ 



where A^ = number of turns in the coil. 



Equation 10.9 shows that the generated voltage will be independent of 

 the frequency if the velocity of the armature is independentof thefrequency. 



The equivalent circuit of the mechanical system is shown in Fig. 10.9, 

 Damping, represented by the compliance Cmi and the mechanical resis- 

 tance Ymxi is furnished by a suitable material such as viscoloid. The re- 



