How the Cochlea Hears: The Physics of Basilar Membrane Resonance

Anatomy of the cochlea

The cochlea is a bony, snail-shaped canal wound roughly two and a half turns, embedded in the temporal bone of the skull. Along most of its length it is divided into three fluid-filled compartments by two membranes: the basilar membrane (below) and Reissner's membrane (above). The scala vestibuli sits at the top, the scala tympani at the bottom, and the middle compartment — the scala media — contains endolymph, a fluid with an unusually high potassium concentration (~150 mM K⁺) maintained by the stria vascularis.

The stria vascularis generates a resting DC voltage of about +80 mV inside the scala media relative to the surrounding perilymph — the endocochlear potential — which drives mechanotransduction. Hair cells sit on the basilar membrane within the organ of Corti, their stereocilia in contact with the overlying tectorial membrane. There are roughly 3,500 inner hair cells (IHCs) in a single row, and about 12,000 outer hair cells (OHCs) in three rows.

The travelling wave and tonotopic mapping

Sound enters the cochlea as a pressure wave via the stapes footplate pressing on the oval window, forcing the basilar membrane to deflect. That disturbance does not resonate the whole membrane at once — it propagates as a travelling wave from base to apex, exactly as Georg von Békésy observed in cadaver cochleae (Nobel Prize, 1961). The membrane is narrow (~0.1 mm) and very stiff at the base, wide (~0.5 mm) and flexible at the apex, with stiffness falling roughly exponentially — by a factor of about 10,000 — over its 35 mm length.

f(x) = f_base × exp(−x / d)
f_base ≈ 20,000 Hz (base, x = 0)   f_apex ≈ 20 Hz (apex, x = 35 mm)
d ≈ 7 mm (space constant; each 7 mm halves the characteristic frequency)
Δx / octave ≈ 4–5 mm (the cochlear map is nearly log-linear)

A 1,000 Hz tone produces a travelling wave that peaks about 20 mm from the base. This orderly spatial arrangement of frequency preference is the tonotopic map, preserved through the whole auditory pathway up to Heschl's gyrus — the brain reads pitch by which population of neurons fires most, a place code. The wave envelope is asymmetric, building slowly toward its characteristic place and dropping off steeply beyond it, a shape modelled with the WKB (Wentzel–Kramers–Brillouin) approximation of a slow-varying resonant medium.

Hair cell mechanotransduction

When the basilar membrane deflects, a shearing motion against the tectorial membrane bends the stereocilia bundles on the hair cells. Each hair cell carries a staircase of 50–300 stereocilia joined by fine protein filaments called tip links. Deflection toward the tallest stereocilium stretches the tip links and mechanically opens transducer channels — members of the TMC (transmembrane channel-like) family — letting K⁺ and Ca²⁺ flood in, driven by the electrochemical gradient between endolymph (+80 mV, ~150 mM K⁺) and the hair cell interior (~−60 mV, ~5 mM K⁺).

I_MET = I_max × P_open(x)
P_open(x) = 1 / (1 + A × exp(−x / x₀))
x = stereocilia displacement (nm)   I_max ≈ 1 nA per hair cell at saturation
Half-maximum displacement x₀ ≈ 10–30 nm (extremely sensitive)

The resulting inward current depolarises the inner hair cell, triggering Ca²⁺-dependent glutamate release at the ribbon synapse, which fires the afferent auditory nerve fibre within microseconds. A specialised ribbon structure tethers synaptic vesicles close to the Ca²⁺ channels, allowing release within about 1 ms of stimulus onset.

Active amplification by outer hair cells

Passive mechanics alone produce tuning curves far too broad to explain the sharp frequency selectivity seen in living animals. The missing piece is the cochlear amplifier: outer hair cells can rapidly change length in response to membrane voltage — electromotility — driven by the motor protein prestin (SLC26A5), which shortens or elongates the OHC by up to 4% at audio frequencies. When the basilar membrane moves upward, OHC stereocilia deflect, the cell depolarises, and prestin shortens it — amplifying the membrane's own movement in a positive feedback loop tuned to the local resonant frequency.

At low levels: BM velocity ∝ p           (linear, gain ~1000)
At high levels: BM velocity ∝ p^0.2–0.3  (compressive)
Input SPL 0–120 dB ⇒ BM response spans ~40–50 dB
1 trillion-fold intensity range ⇒ ~300-fold displacement range

This feedback can boost basilar membrane velocity by up to 40 dB (a factor of 100) at low sound levels, with the gain falling at high levels — the compression that lets the ear span a 120 dB dynamic range. The same nonlinearity underlies two-tone suppression, combination tones, and distortion-product otoacoustic emissions, all measurable, non-invasive windows into cochlear function.

Real-world applications

Cochlear implants bypass destroyed hair cells with an electrode array inserted along the scala tympani, driving up to 22 contacts at different positions to exploit the tonotopic map for pitch perception. Hearing aids apply frequency-specific gain to compensate for lost outer hair cell amplification — the most common form of sensorineural hearing loss — using wide dynamic range compression to emulate the cochlea's own nonlinearity. Otoacoustic emissions, sounds produced by the cochlea's active amplifier, are used for universal newborn hearing screening, and the same frequency-analysis principle inspired early analogue filter banks and continues to inform psychoacoustic audio codecs like MP3 and AAC.

Frequently asked questions

Try it live

Everything above runs in your browser — open Cochlea Hearing and watch the travelling wave build toward its characteristic place along the basilar membrane. Nothing is installed, nothing is uploaded.