Interactive visualization of cochlear traveling waves: explore frequency-position mapping on the basilar membrane, tonotopic organization, and the active amplification mechanism
Georg von Békésy (1899–1972) discovered that sound enters the cochlea through the oval window and generates a traveling wave along the basilar membrane. The membrane's stiffness decreases from base to apex — it is about 100× stiffer near the oval window than at the helicotrema. This stiffness gradient causes the wave to slow down and grow in amplitude as it propagates, until it reaches a resonant peak where its frequency matches the local characteristic frequency (CF). High-frequency sounds peak near the base, low-frequency sounds near the apex. This frequency-to-position mapping is called the tonotopic map and earned von Békésy the 1961 Nobel Prize in Physiology or Medicine. The cochlea acts as a biological spectrum analyzer, decomposing complex sounds into their frequency components before neural encoding.
The traveling wave displacement is modeled as: y(x,t) = A(x)·sin(2πf·t − k(x)·x), where x is the position along the basilar membrane (0 = base/oval window, 1 = apex/helicotrema). The characteristic frequency at position x follows the Greenwood function: f(x) = 165.4·(10^(2.1·(1−x)) − 0.88) Hz (for human cochlea, total length ~35mm), covering the full audible range from ~20 Hz at the apex to ~20,000 Hz at the base. The envelope A(x) uses an asymmetric Gaussian model: broader on the base side (wave grows gradually) and narrower on the apex side (sharp cutoff past resonance), with bandwidth Δf = CF/Q controlled by the Q factor. The traveling wave speed decreases toward the resonant peak, causing wavelength compression and amplitude growth. Beyond the peak, the wave is rapidly attenuated as the membrane cannot follow — creating a sharp cutoff.
The cochlea is not a passive filter — outer hair cells (OHCs) act as biological amplifiers through electromotility. When the basilar membrane vibrates, OHCs change their length in response (up to 5% of their body length at kHz rates), injecting energy back into the traveling wave. This cochlear amplifier: (1) increases sensitivity by 40-60 dB, allowing detection of sounds as faint as 0 dB SPL (~20 μPa); (2) sharpens frequency selectivity, with Q values of 5-15 in healthy ears vs 1-3 in damaged ears; (3) produces otoacoustic emissions (OAEs) — sounds generated by the cochlea itself, used clinically to test hearing. The Q factor slider in this visualization simulates this active mechanism: low Q represents OHC damage (as in noise-induced hearing loss or ototoxicity), producing broad, overlapping excitation patterns and poor frequency discrimination. High Q represents healthy cochlear function with sharp, well-separated frequency peaks.
Start with the Pure Tone preset to see a single traveling wave peak on the basilar membrane. The main canvas shows the membrane displacement in real time — notice how the wave travels from base (left, oval window) toward apex (right) and peaks at the resonant position for that frequency. Use the Frequency 1 slider to sweep from 100 Hz to 8000 Hz and observe the peak shift from right (apex, low frequency) to left (base, high frequency). Add harmonics by adjusting Harmonic 2 and 3 sliders — each creates an additional peak at the corresponding position. The Envelope canvas shows the steady-state amplitude envelope for all active components. The Frequency-Position Map canvas displays the Greenwood function mapping frequency to membrane position. Adjust the Q Factor to simulate active cochlear gain: high Q (healthy) gives narrow, sharp peaks; low Q (damaged) gives broad, overlapping peaks — this explains why hearing loss degrades frequency discrimination even when pure-tone thresholds are nearly normal. Try the Vowel /a/ preset to see formant decomposition, and the Major Chord preset to see how musical intervals are spatially separated on the membrane.