New Boundary Conditions and Results for the Peterson-Bogert Model of the Cochlea

Abstract

The Peterson-Bogert model of the cochlea [J. Acoust. Soc. Amer. 22, 369–381 (1950)] specifies, as one of its boundary conditions, zero pressure at the round window. This specification is equivalent to eliminating the round-window membrane. We have changed this boundary condition to include the round-window membrane, representing it with an acoustic compliance. With the new boundary condition, the equation for p+(x) requires a new solution, and a new value of p−(x) at x = 0 is needed. The new solution for p+(x) and the new value of p−(0) are given, for sinusoidal stimulation, as a function of frequency. The latter value is needed as the input to the Peterson-Bogert type of model of the basilar membrane. The model's input impedance as well as the relative displacement between the oval and round windows are also given. These relationships are compared with experimental findings.