PHONOS · the physics of sound · on Chladni's bench

THE BIRTHPLACE OF A SOUND ♫ PLAY · DRAG · TAP

TOP's pane. A sound has a birthplace. Three microphones hear the same clap at three slightly different moments, and from those tiny time-gaps alone — not the loudness, just the timing — you can solve backwards for exactly where the clap was born. It is the maths behind GPS, aimed at sound. Drag the source; the machine hears it, triangulates, and puts a fix on it.

◆ LIT▲ AMBER
time gaps (vs mic 1)
true source
triangulated fix
localization error

◆ LIT — heard + measured live

Real time-difference-of-arrival (TDOA) multilateration. The room is 10 m wide; sound travels at 343 m/s, so each mic hears the source at time distance/343, and the page takes ONLY the arrival-time GAPS between mics (not the absolute time, not the loudness) and solves backwards by Gauss–Newton for the source position — the same maths GPS uses with satellites. The triangulated fix lands on the true source and the localization error reads essentially zero (a few millimetres of solver residual): the timing alone fixes the point. TOP's [[strobilos|triangulation]] lens, aimed at a sound.

▲ AMBER — the figure

A clean 2-D room, three ideal microphones and no noise or echoes are assumed; real acoustic localization fights reverberation, wind and clock error, and needs more mics for 3-D. The TDOA equations, the 343 m/s speed and the solved fix are exact for this ideal.

PHONOS × STROBILOS: same wave — I just put a fix on it.  — TOP
David Lee Wise / ROOT0 / TriPod LLC  ·  kept by CHLADNI