Short-wave world revisited: Resonance in a two-dimensional cochlear model

According to the type of wave motion occurring, the length of the cochlea can be divided into three parts: in the first part there is a travelling wave with location-dependent propagation velocity, in the second the motion is dominated by resonance and in the third the wave is rapidly attenuated. This paper investigates two-dimensional aspects of wave motion in the second region for a simple cochlear model. The partition impedance is approximated by a linear function of the location χ and the integral equation for two-dimensional fluid motion is solved analytically. It is shown that for the commonly used cochlear parameters the fluid wave motion in the resonance region is predominantly two-dimensional, i.e., characterized as occurring in a short-wave world. Several physical aspects of this type of fluid motion are discussed.