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Mechanical waves require an elastic medium to propagate. The speed c_s = (K/) depends on the rigidity and density of the medium: in air (K = 1.4×10 Pa, = 1.2 kg/m³) c_s 340 m/s; in water (K = 2.2 GPa, = 1000 kg/m³) c_s 1480 m/s. This factor 4 difference has profound consequences for aquatic vs. aquatic auditory systems. terrestrial.

The acoustic impedance Z_a = ·c_s is the key factor in reflection/transmission at interfaces: the transmission coefficient T_ac = 4ZZ/(Z+Z)² drops dramatically when Z >> Z or vice versa. At the water-air interface, Z_water/Z_air 3570, so T_ac 0.001 only 0.1% of sound energy passes between both media. The ear of terrestrial mammals has the hammer-anvil-stapes as an impedance transformer to compensate for this loss.

The audible range varies greatly between species: humans 20 Hz 20 kHz, dogs up to 65 kHz, bats 1200 kHz, whales 10 Hz 30 kHz. The upper limit f_max c_s/(2·d_cell) is linked to the processing speed of the hair cells; the lower limit to the size of the hearing apparatus (length of cochlea or membrane).

The Doppler effect f_obs = f_src · c_s/(c_s ± v_src) allows us to estimate the relative velocity of a source. Bats emit pulses and analyze the Doppler shift of the echo to measure prey speed: a moth at 5 m/s produces a shift of f/f v/c_s 1.5%, detectable thanks to the ultra-fine spectral resolution of its specialized cochlea.

The interaural time difference ITD = d·sin()/c_s is the main key to horizontal sound localization. With d 0.18 m and = 90°, ITD_max 530 s in humans. The auditory system detects differences as small as 10 s ( 1°), requiring matching of neural signals with precision of tenths of a microsecond in the superior olivary nucleus.

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