Psychoacoustics: How We Hear

From air pressure to nerve signal

Sound reaches your ear as a pressure wave. The eardrum converts this into mechanical vibration, three tiny bones (malleus, incus, stapes) amplify it, and the fluid-filled cochlea performs a mechanical frequency analysis: its basilar membrane is stiff and narrow near the entrance (resonating at high frequencies, ~20 kHz) and floppy and wide at the far end (resonating near 20 Hz). Different positions along the membrane peak for different frequencies — a tonotopic map, effectively a biological spectrum analyser built from mechanics rather than an FFT.

Hair cells at each position convert local vibration into electrical nerve impulses. From this point on, everything you perceive as "sound" is a construction of the brain from this tonotopic nerve firing pattern — and the construction has systematic, well-mapped biases.

Loudness is not amplitude

Two tones with the same physical sound pressure level (dB SPL) can sound very differently loud depending on their frequency. Human hearing is most sensitive around 2–5 kHz (where the ear canal itself resonates) and far less sensitive at very low and very high frequencies. This is captured by the equal-loudness contours (ISO 226, updating the classic 1933 Fletcher–Munson curves): each contour traces the sound pressure level needed at every frequency to sound as loud as a 1 kHz reference tone.

This is why cheap earbuds sound "thin" at low volume — bass and treble both need much more physical energy than the mid-range to register as equally loud, so as you turn the volume down the extremes disappear first. Consumer audio equipment's "loudness" button compensates for exactly this effect by boosting bass and treble at low playback volumes.

Critical bands & masking

The cochlea does not resolve frequency with infinite precision. It divides the audible range into roughly 24 critical bands (Bark scale), each acting like a band-pass filter with increasing bandwidth at higher centre frequencies (roughly 100 Hz wide below 500 Hz, widening to over 3 kHz above 10 kHz).

Two tones falling within the same critical band interact: a loud tone masks — makes inaudible — a quieter tone nearby in frequency, even though both would be perfectly audible alone. This simultaneous masking also has a temporal counterpart: a loud sound can mask a quiet sound that follows within ~200 ms (forward masking) or, more surprisingly, one that precedes it by up to ~20 ms (backward masking) — the brain needs time to process the loud sound and retroactively "steals" perception from the quieter one.

The missing fundamental

Play harmonics 2, 3, 4, and 5 of a 200 Hz tone (400, 600, 800, 1000 Hz) through a tiny speaker that physically cannot reproduce 200 Hz at all. You will still hear a pitch of 200 Hz — the brain infers the missing fundamental from the spacing between the harmonics that are present, because that spacing (200 Hz) is the only fundamental frequency consistent with the harmonic series it's hearing.

This is exactly how small phone and laptop speakers, physically incapable of producing deep bass, still let you perceive a bassline — psychoacoustic bass enhancement processors deliberately synthesise upper harmonics of missing low frequencies to exploit this illusion.

How two ears locate a sound

With only two ears, the brain locates a sound source in 3D using three main cues:

• Interaural Time Difference (ITD) — a sound from the left reaches the left ear before the right. Below ~1.5 kHz the brain resolves this timing difference directly (down to ~10 microseconds of resolution — better timing precision than almost any other biological sense).
• Interaural Level Difference (ILD) — the head casts an acoustic "shadow"; above ~1.5 kHz, wavelengths are short enough that the head significantly attenuates sound reaching the far ear, and the brain uses this level difference instead.
• Spectral cues (pinna filtering) — the folds of the outer ear filter sound differently depending on elevation and front/back position, resolving the up/down and front/back ambiguity that ITD and ILD alone cannot (both give identical cues for a "cone of confusion" of directions).

Why MP3 works

Lossy audio codecs (MP3, AAC, Ogg Vorbis) are built almost entirely on psychoacoustic masking. The encoder runs an FFT to find the spectrum, splits it into critical bands, computes the masking threshold in each band from the louder neighbouring content, and then allocates just enough bits to keep the quantisation noise below that masking threshold — noise the ear is mathematically guaranteed not to notice. Content with strong tonal masking (a loud bass note, for instance) can shed enormous amounts of data in nearby frequency bands with zero perceived quality loss.

Try it yourself

See standing waves and resonant patterns form directly on a vibrating plate — a physical, visual analogue of how the cochlea's basilar membrane resonates at different positions for different frequencies: