A possibility of sharp tuning in a linear transversally inhomogeneous cochlear model

Considerable sharpening of basilar membrane frequency selectivity and simultaneous decreasing of phase lag can be obtained in a linear ('passive') hydromechanical three-dimensional cochlear model, if the transverse geometry of the cochlea is taken into account. Both the tuning qualities, Q10, and the phase angles at CF of some transversally inhomogeneous linear models can be set into the range of experimental data [Sellick et al. (1983) Hear. Res. 10, 93-108; Robles et al. (1986) J. Acoust. Soc. Am. 80, 1364-1379.] The calculations are developed on the base of WKB-approximation. The integral coefficients of eiconal equation are the transversally averaged means of basilar membrane surface mass density and stiffness: (formula; see text) where eta(y) is the major eigenfunction of basilar membrane cross-sectional vibrations. The classical Ritz's method is used for calculation of the cross-sectional eigenfunctions. The size and the form of cochlear cross-section are found also to alter the tuning. The rapid increase of the model response towards the peak is due to that damping remains negligible up to the peak position, where the imaginery part of the wave-number begins to increase sharply.