Linear cochlear mechanics.

An active, three-dimensional, short-wavelength model of cochlear mechanics is derived from an older, one-dimensional, long-wavelength model containing time-delay forces. Remarkably, the long-wavelength model with nonlocal temporal interactions behaves like a short-wavelength model with instantaneous interactions. The cochlear oscillators are driven both by the pressure and its time derivative, the latter presumably a proxy for forces contributed by outer hair cells. The admittance in the short-wavelength region is used to find an integral representation of the transfer function valid for all wavelengths. There are only two free parameters: the pole position in the complex frequency plane of the admittance, and the slope of the transfer-function phase at low frequencies. The new model predicts a dip in amplitude and a corresponding rapid drop in phase, past the peak of the traveling wave. Linear models may be compared by their wavelengths, and if they have the same dimension, by the singularity structure of their admittances.