Beats in Cochlear Models

Abstract

Particle motion within the fluids of cochlear models occurs in elliptical orbits which are essentially Lissajou figures caused by interaction between the (forced) stapedial motion and the (induced) motion of the cochlear partition [J. Acoust. Soc. Am. 29, 558 (1957)]. In response to beats these orbits were found to wax and wane synchronously with the beat frequency. However, the alternating waxing and waning was not symmetrically centered about the orbital midpoints. In scala vestibuli, the orbits invariably expanded farther in the apical than in the fenestral direction. In scala tympani, the directions were reversed. Thus a partial rectification occurred within the cochlear fluids which, being synchronized with the beat rate, was of opposite direction in both perilymphatic scalae. This manifestation of energy at the beat frequency had to be due to some nonlinear property of the model, since no energy occurs at this frequency in linear systems. The nonlinear property was finally identified as the stiffness gradient of the cochlear partition. The resulting beat amplitude (re particle amplitude of a given set of primaries) was directly related to the steepness of the stiffness gradient. Furthermore, the beat amplitude reflected upon the shape of the gradient at various locations along the partition when beats (of a constant rate) were produced by different sets of primaries. [This research was supported in full by the U. S. Air Force under contract number AF 41 (657)-148, monitored by the School of Aviation Medicine, U. S. Air Force, Randolph Air Force Base, Texas.]