2 IS 



BELL SYSTEM TECHNICAL JOi'RNAL 



taking into account all major external as well as internal reactions, 

 mav then be written: 







dix 

 'dt 



A^ + R,H + Gh + K,^q,+ ^"'^'" -• ' ""^^ 



^'o^ 



ZqSiSo 



^1 H rr-TT— ^2 



6'o^ 



di 



■'^n^j'i" • , JunOiOt . 



i) = Lo-f-\- R2i2 + A'og. - Gi\ + -^~- k + 





t,. 



(26) 



(27) 



These equations may be put in a somewhat simpler form by virtue 

 of the fact that they are linear differential equations with constant 

 coefficients. In such a case the time differential may be replaced 

 by an algebraic operator p such that i = pq, di/dt = p^q, where p is 

 of the dimensions and nature of a frequency 



= ifU + pR: + pZof,]qx +(pG + pZ,^+K„^q,, (28) 



= (- pG + pZo^ jq, 



+ ( p-U + pR-i + K. + />Zo|^; 

 The determinant of this system is (calling pZ^ = Fo) 



(29) 



D 



p'L, + pR, + Yo-^^pG + Yo^ + A'„ 



- pG+ Yn^)U-'L. + PR, + Ao + F„|^n 



(.SO) 



This determinant represents the complete reactions of the larynx and 

 the external effects of communicating air chambers. 



If the effects of the air chambers be disregarded the system is 

 represented by placing Fo == 0, giving the simple form 



D 



(p'U + pRi) 

 - pG 



ipG + K„) 

 ip-Lo + pR.2 + K.) 



(31) 



Nature of This System 



The voice system represented by determinant (3) is very closely 

 analogous to other vibrators, such as the microphone oscillator or 

 door buzzer and the vacuum tube oscillator. The literature on the 

 latter subject is now so extensive that the pointing out of the analogy 

 should make the method of solution for sustained oscillation, as in 

 singing, or for subsidence or accretion of the oscillation, as in speak- 

 ing, clear to any one familiar with it. 



