Cochlear frequency analysis: the basilar-membrane place-map

The basilar membrane maps frequency to place: Greenwood's function f = 165.4·(10^{2.1x} − 0.88) runs from about 19.8 Hz at the apex to 20.7 kHz at the base, reproduced here. This is a classical resonant filter bank, cited not re-derived; the hair cell at each place is the R19 mechanotransduction switch that converts deflection into current.

Cochlear frequency analysis is place-coding: the stiffness-graded basilar membrane resonates at a position-dependent frequency, and Greenwood's 1990 human function reproduces the ~20 Hz–20 kHz range (apex 19.8 Hz, base 20677 Hz). The place-map is a cited classical anchor [L] reproduced by arithmetic [V-arith]; mechanotransduction at each place is the R19 gating-spring switch.

The cochlea analyses sound by position, not by timing alone: stiffness falls smoothly from base to apex, so each place along the basilar membrane resonates best at its own frequency. High frequencies peak near the stiff base; low frequencies near the compliant apex. This is tonotopy, and it is why the ear is, in effect, a mechanical spectrum analyser.

The human map spans three decades of frequency

Greenwood's frequency–position function reproduces a range from about 19.8 Hz at the apex to 20677 Hz at the base, matching the familiar ~20 Hz–20 kHz span of human hearing. The map is a cited classical anchor that the package reproduces arithmetically; the membrane mechanics themselves are not re-derived from the substrate.

What converts membrane motion into a nerve signal?

At each place, the mechanical deflection is turned into electrical current by the hair-cell mechanotransduction (MET) channel — a two-state, gating-spring gate. That gate is shown to be an R19 double-well in the unified-transducer chapter, and the active force that sharpens and amplifies the response sits at a critical point, derived in the cochlear amplifier.