The cochlear compromise

TLDR: It is conjectured that the design of the cochlea is influenced by two conflicting requirements: (1) the coChlea should act as a precise frequency analyzer and (2) waves propagating along the basilar membrane should be transmitted without reflections.

Abstract: It is conjectured that the design of the cochlea is influenced by two conflicting requirements: (1) the cochlea should act as a precise frequency analyzer and (2) waves propagating along the basilar membrane should be transmitted without reflections. Accurate frequency analysis is possible only if the mechanical properties of the cochlea change rapidly with distance along the basilar membrane. Reflections of waves traveling on the basilar membrane will be negligible, however, only if these same mechanical properties change slowly. A compromise between these two requirements is possible if a loss constant δ related to the sharpness of response of the basilar membrane to a pure tone is related to the number N of wavelengths of the wave on the basilar membrane [N/(δ)1/2?1]. Furthermore, if sizable changes in the displacement occur only over distances larger than the width of a hair cell, then δ must be larger than the ratio of the width w of a hair cell to the distance d along the basilar membrane over which...