A basilar-papilla hair cell tuned to has a bundle stiffness at body temperature

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

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

Problem

A basilar-papilla hair cell tuned to

f_0 = 6\,\mathrm{kHz}

has a bundle stiffness

\kappa = 3.0\,\mathrm{mN\,m^{-1}}

at body temperature

310\,\mathrm{K}

. Its transduction current is filtered to an effective bandwidth

f_0/Q

with

Q = 12

. ((a)) Using equipartition for the bundle's single mechanical degree of freedom, find its total rms thermal displacement. ((b)) Taking the bundle's thermal noise to be spread roughly evenly over a band about as wide as

f_0

, find the rms displacement noise that passes the

Q=12

filter. ((c)) A tone near threshold deflects the bundle by about

1.0\,\mathrm{nm}

rms. Find the ratio of this signal to the band-limited noise from part (b) and, taking a signal-to-noise ratio of about

3

as the criterion for reliable detection, state whether the tone is detectable.

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