Theory of Vibration of the Larynx^ 



By R. L. WEGEL 



The vibration in the larynx is caused by an automatic modulation by 

 the vocal cords of the air stream from the lungs. Analytically the mechan- 

 ism is the same, and physically, closely analogous to that of the vacuum 

 tube oscillator. It depends principally on the resonance of the vocal 

 cords, the modulation of air friction in the glottis by their motion and 

 the attraction due to constriction of the air stream between them. When 

 these forces exist in certain relative proportions and phases, sustained 

 oscillation as in singing takes place. The whole mechanism may be rep- 

 resented analytically b>' force equations, from which conditions for accre- 

 tion or subsidence of the vibration or for sustained oscillation may be 

 easily deduced. These equations also show the analogy with other types 

 of oscillating systems. 



IT is customary in treating the theory of the voice to assume the 

 glottis or space between the vocal cords to be a source of a steady 

 stream of air with superimposed periodic impulses caused by the 

 vibration of the vocal cords. The harmonic content of these impulses 

 is modified by the "resonating" vocal cavities before being radiated 

 into free air. It is the nature of this modification which receives most 

 attention. The mechanism by which the vibration of the vocal cords 

 is maintained has not been carefully studied. 



The vocal cords are maintained in a state of sustained vibration 

 by the proper balance between the various mechanical constants of 

 the complete system, which thus act as a transformer of a part of 

 the non-vibratory power derived from the air stream from the lungs 

 into the vibratory power resulting in sound. It is a simple theory 

 of this mechanism which is considered here. 



The method used is to obtain the force equations, which describe 

 the vibrations of the complete mechanical system, by means of the 

 Lagrange equations, from expressions of the total instantaneous 

 kinetic and potential energies, the instantaneous forces acting and 

 rate of dissipation of energy. The resulting simultaneous equations 

 relating to the displacements and velocities of the various parts are 

 then studied to find the frequencies of free vibration and the relations 

 which must obtain between the various mechanical parameters of 

 the system in order that one of these frequencies be sustained. The 

 method is an application of the theory of H. W. Nichols, published in 

 Physical Revinv, August, 1917. 



The theory is reduced to easily workable form by the introduction 

 of simplifying approximations which will be described in the progress 



1 Presented before Acoustical Society of America, May 11, 1929. 



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