452 KENNELLY, TAYLOR— PROPERTIES OF 



APPENDIX II. 



Outline Theory of the Absorption Diagram. 



The following provisional theory was arrived at by searching 

 for a quantitative expression that would satisfy the impedance dia- 

 grams when distortion was present. It bears a close analogy to the 

 theory of alternating-current coupled circuits in the steady state. 



The equation for the ordinary motional-impedance circle, con- 

 sidered as representing a vibration velocity circle, and neglecting the 

 depression angles ;8i° and /?„° is^*' 



AI F F ,. ,. / , s 



Xm, = — = — = ;;- max. cyclic kmes Z , (23) 



(mco-^) 



where 



F = AI =^the maximum cyclic V.M.F. to standard phase, dynes Z , 



A = force constant of the receiver, dynes/absampere, 

 / = maximum cyclic current strength, absamperes, 

 r = mechanical resistance of diaphragm, dynes/kine, 



w = equivalent mass of diaphragm, gm., 

 J r= elastic constant of diaphragm, dynes/cm., 

 ^^ = mechanical impedance, dynes/kine /_, 

 M^^ 21711, impressed angular velocity, radians/sec, 



mq = resonant angular velocity, radians/sec, 

 w ^impressed frequency, cycles/sec, 



Wq = resonant frequency, cycles/sec, 



y= V— I, 



;i-,„ ^ mechanical displacement amplitude of diaphragm, 



max. cyclic cm. Z , 

 ;t:„i = vibrational velocity of diaphragm, max. cy. kines Z • 



When the vibrating diaphragm supplies motional power to a 

 dependent vibrational system, having its own natural frequency n^., 

 and therefore its own mechanical constants s^, nu, r^_ and Sn, the de- 

 pendent or secondary system will exert a max. cyclic counter vibro- 

 motive force (C. V.M.F.) — /„, on the driving force F ; so that the 

 resulting equation of motion becomes 



If' Bibliography, 9. 



