A model for vocal cord excitation

This paper reports the results of an experimental and analytical investigation of a possible mechanism for exciting vibrations of the vocal cords. In order to test various approximations for describing the flow past the vocal cords and to demonstrate the importance of the upstream impedance in the excitation mechanism, the vocal cords are first represented by the simplest possible model, namely a simple vibrator of fixed shape. It is shown that if the pressures at the upstream and downstream ends of the channel formed by the vibrator wall are constant, the aerodynamic forces take energy from the vibrational motion. If, on the other hand, the output impedance of the system upstream of the channel is negative imaginary, vibrations of the channel walls can be excited. Experimental results agree with the predictions of the flow analysis for the simple vibrator. It is then argued that the respiratory system upstream of the larynx can be described as a tube 20 cm long in which the wave speed is reduced because of the distensibility of the bronchi, and which opens into the large reservoir of the lungs. Results of experiments in which the input impedance at the mouth was measured are consistent with this description. With this upstream impedance it is found that the simple vibrator would only be excited in a limited frequency range and would not allow many of the significant features of the vocal cord vibrations to be represented. Consequently a two-degree-of-freedom model for the vocal cords is introduced. The flow analysis and impedance description are used in calculating the forces acting on the two-mass model. It is predicted from the model that vibrations of the vocal vords are self excited over a range of frequencies. The properties of the self-excited oscillations described by the model agree with the observed properties of the self-excited vibrations in an experiment using a rubber membrane to represent the vocal cord, and are also consistent with several properties of the voice.