Illustrated Physics
physics, drawn
Concept

Aliasing — where it appears

A false, low frequency that appears when a signal is sampled too slowly to follow it. The samples trace the difference between the signal's frequency and a multiple of the sampling rate, which makes wagon wheels turn backwards on film, folds a pulsed radar's speeds and shows as moiré when pixels photograph fine stripes.

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

A tornado's winds, folded. The radial wind across a line through the centre of a tornado-like vortex 400 m across with peak winds of 60 m/s — towards the radar on one side, away on the other — as it truly is (grey) and as a radar with a Nyquist velocity of ±25 m/s reports it (red). Outside the core the winds are slower than 25 m/s and are reported correctly. Near the core they exceed it, and the reported speed folds over: the strongest inbound winds appear as outbound and the outbound as inbound, so the tight pair of opposite velocities that marks a tornado — the velocity couplet — is turned inside out. Forecasters and the algorithms they use learn to read the sharp jumps between neighbouring gates as folds rather than winds, and to unfold them by continuity from the slower winds around.

The speeds a pulsed radar folds into one

A weather radar measures the wind inside a storm by the Doppler shift of its echoes, but it never hears the shift itself. It listens in pulses, and between pulses it notes only how far the echo's phase has turned — which is known only to within a whole turn. So speeds that differ by a fixed amount give identical echoes, and every speed is folded into a window. Make the window wider by pulsing faster, and the echoes from distant rain arrive after the next pulse has gone and land at the wrong range. The two limits multiply to a constant the designer cannot touch.

waves · Doppler Two fine gratings that make a coarse one. Top: two gratings of dark bars laid over each other, one with a period of 10 units and the other of 11, both with bars half a period wide. Bottom: the average transmission of the pair, smoothed over a few periods. Where the bars of the two gratings coincide, light passes through the gaps between them; where the bars of one fill the gaps of the other, nothing passes. The two drift in and out of step once every 110 units — the moiré period, p₁p₂/|p₁ − p₂| — producing broad dark and light bands 11 times coarser than either grating. Neither grating contains a period of 110; their product does.

The pattern two gratings make that neither contains

Lay one fine net curtain over another and broad, swirling bands appear that are in neither curtain. Two sets of lines a tenth of a millimetre apart, differing by one part in a hundred, make bands a centimetre apart. This is moiré: the beat of two gratings in space, as two notes a little out of tune beat in time. It magnifies whatever makes the gratings differ — a twist, a stretch, a shift — by the ratio of the bands to the lines, so it is used to measure strain in bridges and to align the layers of microchips. And two sheets of carbon, twisted by just over one degree, make a moiré on which electrons stop moving and the material superconducts.

waves · Superposition

Named alongside it

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

AmbiguityBeatsDiffraction gratingDoppler effectGrapheneMoire patternNyquist frequencyPhasePulse repetition frequencyRadarSamplingStrain

All concepts