Auditory Perception in Flatland: The Physical Applicability of a Two-Dimensional Cochlear Model

The basilar membrane is a small structure threaded through the cochlea that assists in converting atmospheric pressure oscillations into auditory sensation. Following the example of an existing model, the Navier-Stokes equations of fluid motion, Fourier transforms, and numerical approximations are used to model the basilar membrane as a function of place, time, and input frequency. For simple sound waves, the model adequately predicts locations of resonant frequencies on the basilar membrane, but it fails to represent the fine details of traveling waves, and it does not specify the magnitude of membrane displacement. For complex sound waves, the model accurately reflects the responses of non-living cochleas, but it is not equipped to assess the responses of living ones