Storyboard

Every physical signal degrades during its propagation by two mechanisms: geometric attenuation (dilution of energy with increasing r, 1/r² law) and absorption (conversion of wave energy into heat, exp(-r) factor). The combination produces I(r) exp(-2r)/r², which drops much faster than either mechanism alone.

Noise is the fundamental limit of any sensor: even at room temperature (T = 300 K), thermal agitation generates voltage fluctuations S_v(f) = 4k_BT·Re[Z] in any electrical or mechanical resistance. In neurons, this Johnson-Nyquist noise competes with weaker signals, setting the minimum threshold for biological detection.

The SNR = P_signal/(k_BT·B) shows that sensitivity can be improved by reducing the temperature T (endothermy helps, but living beings have T > 273 K) or by reducing the bandwidth B (more frequency selective sensors). Tuned filters of the ears (basilar membrane) and eyes (color filters) are biological implementations of this strategy.

The time-frequency uncertainty principle t·f 1/(4) establishes that you cannot simultaneously have high temporal resolution and high spectral resolution: a very brief sound ('click') has a very wide spectrum; a pure note has a long duration. This limits the temporal localization of sound sources and simultaneous tonal discrimination.

Dispersion in non-ideal media (d²k/d²) broadens the pulses as they propagate: each frequency travels at a slightly different speed. In the eye, the chromatic dispersion of the lens is partially compensated by the distribution of cones. In biological sonar systems (bats, dolphins), the aquatic or aerial environment introduces minimal dispersion, preserving the temporal resolution of the pulse.

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ID:('ky', 570)

Description

ID:(0, 570)