The Cochlea: How a Fluid-Filled Coil Sorts Sound into Pitch

A frequency analyser made of fluid and membrane

The cochlea is a fluid-filled spiral about the size of a pea, and it does something no electronic filter bank does as elegantly: it sorts an incoming sound into its component frequencies purely through the mechanics of a tapered membrane, before a single nerve signal is fired. The theory that explains it, place theory, says that each frequency has its own physical address along the cochlea's length.

Why the basilar membrane sorts frequencies

Running down the centre of the cochlea is the basilar membrane, and its mechanical properties change continuously along its length: near the oval window (the base) it is narrow and stiff; near the tip (the apex) it is wide and floppy. Stiffness and mass together set a local resonant frequency, so the base resonates best to high frequencies and the apex to low ones — a stiffness gradient turned into a frequency map, entirely passively.

When a sound enters, pressure waves in the cochlear fluid set the whole basilar membrane moving as a travelling wave, first described by Georg von Békésy (Nobel Prize, 1961). The wave starts at the base and moves toward the apex, growing in amplitude as it goes — but only up to a point. At the position where the membrane's local resonant frequency matches the sound's frequency, the wave reaches a sharp peak and then dies away rapidly past that point. High frequencies peak near the base; low frequencies travel almost the full length before peaking near the apex.

The Greenwood function: mapping place to frequency

The relationship between position and frequency is not linear — it is close to logarithmic, and for the human cochlea it is captured well by the Greenwood function, published by Donald Greenwood in 1961 and refined in 1990:

f(x) = A . (10^(a.x) - k)

x  = fractional distance along the basilar membrane, 0 (apex) to 1 (base)
A  = 165.4 Hz,  a = 2.1,  k = 0.88     (typical human constants)

Plug x = 1 (the base) into this formula for a human cochlea and you get roughly 20 kHz, the top of human hearing; x = 0 (the apex) gives close to 20 Hz. Because the exponent is linear in x while frequency itself is exponential in x, equal physical distances along the membrane correspond to equal ratios of frequency, not equal differences — a musical, logarithmic map that lines up closely with how pitch is actually perceived (an octave is a fixed physical distance no matter which octave it is).

Active amplification: it is not a passive filter

A purely passive membrane, driven only by fluid pressure, would produce a broad, gently tapering peak — not sharp enough to explain how finely humans discriminate pitch. The missing sharpening comes from outer hair cells sitting on the membrane, which contract and expand in sync with the local vibration (a process called electromotility) and mechanically pump energy back into the travelling wave right at its peak. This 'cochlear amplifier' boosts quiet sounds by up to 40-60 dB, sharpens the frequency tuning by an order of magnitude compared to a passive membrane, and is also the source of otoacoustic emissions — faint sounds the healthy ear itself emits, used clinically to test hearing in newborns.

Inner hair cells, positioned along the same membrane, are the actual sensory transducers: as the membrane moves, tiny stereocilia bundles on top of each inner hair cell are deflected, opening mechanically gated ion channels and triggering a nerve impulse. Because each inner hair cell sits at a specific place, and place encodes frequency, the auditory nerve fibre attached to it is 'tuned' to that frequency before any neural processing happens at all — the tonotopic map is preserved from the cochlea all the way up through the brainstem to the auditory cortex.

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