Critical Bandwidth and the Frequency Coordinates of the Basilar Membrane

Abstract

Masked audiograms were used to measure critical bandwidth. On the assumption that critical bands represent equal distances on the basilar membrane and that critical bandwidth increases exponentially with distance from the helicotrema, functions were derived which (1) relate critical bandwidth to frequency and to position on the basilar membrane and (2) relate position of maximum amplitude to frequency. The functions are consistent with Békésy's optical observations and Mayer's psychophysical data. The frequency-position function is f = A (10ax − 1). The coefficient a is numerically identical with the coefficient in the exponential function fitting Békésy's elasticity data. Functions of this form fit data from seven other species and the values of the coefficient a seem related to their respective elasticity, functions The interpretation of critical bandwidth as the frequency interval over which the cochlea sums power is supported by data of Mayer, and the hypothesis that critical bands represent equal distances on the basilar membrane is strengthened, one critical band corresponding to one millimeter. Problems for cochlear theory are posed (1) by the apparent equivalence of critical bandwidth, the derivative of the frequency-position function, and the frequency interval over which spatial integration takes place, and (2) by the proportionality of these three at a given point to the compliance at that point.