High-frequency rolloff in a cochlear model without critical-layer resonance.

Abstract

Zwislocki's original cochlear model, incorporating axial fluid inertia and shunt basilar-membrane stiffness and viscous resistance, possesses an operating regime not previously emphasized in the literature. Even in the absence of basilar-membrane mass and the consequent critical-layer resonance, this regime provides extraordinarily steep high-frequency rolloff. That rolloff is not associated with a critical frequency at which energy flow velocity goes to zero, but is attributable instead to a combination of two effects; (1) frequency-dependent energy coupling to the basilar-membrane viscous resistance, leading to local attenuation of the traveling wave at a rate (Np/cycle) that is directly proportional to frequency, and (2) wavelength that decreases with increasing frequency, thus increasing the number of cycles per unit length of basilar membrane. This combination leads to local attenuation of the traveling-wave amplitude (hence energy absorption from the traveling wave) that is strongly dependent on frequency, the rate (Np/cm) being proportional to the square of frequency in the long-wave mode. In Ranke's (two-dimensional, short-wave mode) version of the model, the same operating regime leads to attenuation that is even more intensely dependent on frequency, the rate being proportional to the cube of frequency.