Ranke Revisited—a Simple Short-Wave Cochlear Model

Abstract

Between 1931 and 1950, Otto F. Ranke published an extended series of papers on cochlear dynamics. Much of this work concerned the only published mathematical attempt (prior to the recent paper by Lesser and Berkley) to avoid the long-wave assumption accepted for mathematical convenience by every other analyst (e.g., Zwislocki). Ranke's short-wave analysis is often referenced but has been otherwise largely ignored—perhaps partly because his more comprehensive papers are in German, use rather clumsy mathematical techniques, and are full of errors. This situation is regrettable since evidence of many kinds suggests that the short-wave assumption is more reasonable than the alternate in all but the more basal parts of the cochlea at all but very low frequencies. Moreover, in the modern form described in this paper, Ranke's analysis is extremely simple and transparent, yielding virtually closed-form expressions for the important cochlear quantities. It thus helps to explain many aspects of normal and abnormal cochlear behavior, as well as to account for such features as the extraordinary insensitivity of this behavior to the way in which the system is driven (e.g., Békésy's “paradoxical motion” and bone conduction).