The Greenwood function for the human cochlea is f = 165.4 (10^ 2.1x - 0.88 ) , Hz

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Bioelectricity, the senses and the physics of the body · Bioelectricity, the senses and the physics of the body

Forces, Machines and Signals, Ch Hearing: from air pressure to a gated channel

Problem

The Greenwood function for the human cochlea is

f = 165.4\left(10^{2.1x} - 0.88\right)\,\mathrm{Hz},

where

x

runs from

0

at the apex to

1

at the base of a basilar membrane of length

35\,\mathrm{mm}

. ((a)) Find the fractional position

x

at which a

4000\,\mathrm{Hz}

tone peaks. ((b)) Convert this to a distance from the apex in millimetres.

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