THEORY OF VIBRATION OF THE LARYNX 211 



the vocal cords from an appropriately chosen reference position, L^ 

 their inertia coefficient and K^ their effective stiffness, all measured 

 at the tips, the total kinetic energy, T, and potential energy, V, of 

 the larynx are 



T = hL,'(A + hy + H2^2^ (2) 



V = ^K,(Q2 + 92)-. (3) 



The Lagrange equation of forces for the nth coordinate of any 



system is 



_ddT_dT dV 



dtdtn dqn dqn, 



in which Fn is a reaction due to friction. The force equations for 

 the glottis and vocal cords therefore become 



17 P I ^ ^ 



dt dti 



hU'ih + hY 



(5) 



^ = ^^^ + ^^ + ^^^^^ + ^^^ 2 ^ • ^^^ 



Nature of the "Constants" of the System 



It is quite safe to conclude that none of the coefficients (inertia, 

 dissipation and stiffness) of the larynx are sensibly constant over the 

 range of operation of the coordinates. Direct measurements are 

 evidently impossible. It is conceivable that they may be arrived at 

 indirectly by means of a comparison of experimental data, especially 

 taken for the purpose, on voice curves and the results of dynamic 

 analysis of the kind described here. The problem may also be studied 

 by means of models. In order to solve equations 5 and 6 it is, how- 

 ever, necessary to evaluate the space and velocity derivatives. 



A few simple experiments were performed on models for the sole 

 purpose of determining the qualitative nature of variation of resistance 

 of the glottis with displacement of the vocal cords. A diagram of 

 the model used in the measurements is shown in Fig. 3. This con- 

 sists of a brass tube, a, ^i" in diameter, beveled off on the top at an 

 angle of 45° with the axis, and two 3 s" brass plates, h, fitted on these 

 beveled surfaces so as to leave a slit, S, which was made adjustable 

 in width. A cross-section of this model is shown in c. The bottom 

 of the tube was attached to a large air chamber in which the pressure 

 and velocity of air flow could be regulated and measured. 



Three shapes of "glottis" were measured. The first had square 

 corners, as shown on Fig. 3f. The second, M, was the same as ic, 



