Theory of Vibration of the Larynx

T 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 " r e s o n a t i n g " 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.