Illustrated Physics
physics, drawn
Concept

Diffuse field — where it appears

A wave field in which energy flows equally in every direction, as in a reverberant room or ground shaken by sources all around. In such a field the correlation of the motion at two points reproduces the wave that would travel between them, which is how noise maps the Earth's crust.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Where cancelling a 500 Hz tone works. Sound at 500 Hz (wavelength 69 cm) arriving from every direction at random, as it does in a room or a cabin, and a small loudspeaker 50 cm to the left of a microphone (black dot), driven to cancel the sound exactly at the microphone. Contours mark where the sum is 20 dB quieter than the original (red), 10 dB quieter (blue), unchanged (grey) and 6 dB louder (black), in a plane through both. The zone at least 10 dB quieter is 12.0 cm across, at right angles to the line from speaker to microphone — 0.18 of a wavelength — and beyond the unchanged contour the cancelling source only adds sound. Silence has been made at a point, not in a room.

The silence that fits in a tenth of a wavelength

Two sounds of equal strength and opposite phase add to nothing, so any noise can be cancelled by playing its inverse. At one point. A microphone and a loudspeaker can silence the air exactly where the microphone is, and nowhere else for certain: in the diffuse sound of a room the quiet zone is a few tenths of a wavelength across, under ten centimetres at a kilohertz, and beyond it the cancelling speaker only adds noise. That is why noise cancellation works in a headphone and not in a room, and why it works on the drone of an engine and not on a voice.

waves · Superposition A pulse that comes out of the average. The cross-correlation of the two stations' records against lag, in seconds: for single sources at 0°, 45° and 90° from the line through the stations, each a copy of the noise's own ten-second wavelet shifted to that source's arrival difference — 20.0 s, 14.1 s and 0 s — and the average over all 720 sources round the ring, scaled up 9-fold to share the axes. The single-source correlations are wherever their geometry puts them. The average has peaks at ±20 s, the time a wave takes to cross 60 km at 3 km/s, one for travel from A to B and one from B to A, and little between them. That pulse is the signal a seismometer at B would have recorded had an earthquake happened at A: the Green's function between the stations, recovered from noise that never came from either.

The echo hidden in random noise

A seismometer that is not recording an earthquake is not recording silence. It hears the Earth's hum: the pounding of ocean waves on every coast, arriving from all directions as surface waves with periods near ten seconds, indistinguishable from random noise. Two seismometers sixty kilometres apart hear different noise. Yet if their records are correlated and averaged over hours, a pulse appears at a lag of twenty seconds — the time a wave takes to travel from one to the other — exactly as if an earthquake had happened under one station and been recorded at the other. Noise from everywhere contains the echo between any two points, and since 2005 seismologists have mapped the Earth's crust with it.

waves · Guided waves

Named alongside it

The objects these essays reach for when they reach for this one.

Active noise controlCausalityCross correlationDestructive interferenceGreens functionMonopoleSeismic noiseSound pressureStationary phaseSuperpositionSurface waveTime reversal

All concepts