21-1 BELL SYSTEM TECHNICAL JOURNAL 



It might be seen by carrying through an expression for this glottis 

 mass involving a function of velocity similar to that for R of equa- 

 tion (7) that only a quantitative change in effective mass would 

 result in the final equations and that no new type of reaction would 

 be introduced. This demonstration is not included here. In order 

 to save space in this qualitative treatment it is ignored. For small 

 displacements go from a reference position at which the velocity of 

 the air is /o, the glottis inertia may be represented by the direct 

 function: 



Ly = Li +-3— ^2 + ^^-^^2- + etc., (11) 



in which the coefficient of 92 is obviously positive. The second term 

 of the second member of (5) may now be evaluated by performing 

 the differentiations as indicated. Neglecting second and higher order 

 terms and denoting dq^/dt by /n the reaction in question becomes 



The glottis mass of air, therefore, introduces two kinds of reactions: 

 a simple inertia and a reaction proportional to the velocity of the vocal 

 cords. For simplicity of notation (12) will be written 



Uf^ + Gi,. (13) 



This completes the evaluation of the terms (5), the force equation 

 of the glottis, which may now be written 



£0 == Roh + RJ, + K,.q, + ^ + Gu. (14) 



Force Equation' of the \'ocal Cords 



The force equation (6) of the vocal cords contains four terms. The 

 first is the inertia reactance of the vibrating lips. The mass Lo is 

 the effective vibrating mass which, if multiplied by one-half the square 

 of the velocity at the cord tip, gives the kinetic energy of their motion. 

 If the distribution of the velocity in the vocal cords were known 

 this might be found by integration. The second term Fo in equa- 

 tion (6) represents the internal dissipation and is assumed propor- 

 tional to the small velocity u. The third term is the elastic reaction 

 which is proportional to displacement. 



The fourth term is a " gyrostatic " term. This term ma>- be written 

 as follows: 



