Modal coupling of acoustic wave propagation and mechanical wall vibration in the time-varying vocal tract

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Coupling between acoustic wave propagation and mechanical vibration of wall tissue along the vocal tract has long been considered to be an important loss mechanism in speech, affecting the frequencies and bandwidths of the lower formants. However, the detailed mechanism of energy transfer between fluid and structure as the shape of the vocal tract changes over time has not been fully elucidated. To examine this question, a time-domain finite-volume simulation of quasi-one-dimensional fluid flow and mechanical wall vibration was derived from underlying conservation laws. By calculating the eigenvalues and left and right eigenfunctions of the resulting implicit matrix recursion at each point in time, the sound field can be decomposed into modal vibrations describing coupled motion of air and tissue. Standing waves in the fluid within the vocal tract create sound waves that propagate in the wall tissue. Conversely, standing waves in the wall tissue excite waves in the fluid that propagate as sound. The coupling between airborne and mechanical modes of vibration and the transfer of energy between the two systems can easily be understood by examining the time-varying amplitude and phase of the spatial eigenfunctions. Illustrations are provided for simulations of VCV transitions.