Illustrated Physics
physics, drawn
Concept

Bragg reflection — where it appears

Strong reflection of a wave by a periodic structure at the wavelengths for which the reflections from successive repeats come back in step. The condition is that twice the spacing, projected on the wave's direction, is a whole number of wavelengths; it is how crystals diffract X-rays and layered mirrors reflect one colour.

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

A seabed that reflects one wavelength. The fraction of a surface wave's amplitude reflected by a patch of sinusoidal sandbars 50 m apart and 0.8 m in amplitude, in 4 m of water, against the wavelength of the incoming wave, for 4 bars and 8 bars, from the shallow-water equations integrated through the patch. 4 bars reflect 56 per cent of the amplitude at 99.8 m; 8 bars reflect 86 per cent of the amplitude at 100.4 m, close to twice the bar spacing, where each bar's small reflection returns in step with the others. Away from that wavelength the reflections cancel, and the more bars there are, the narrower the band they reflect.

The sandbars that reflect the sea

A stack of alternating layers reflects the one colour whose half-wavelength matches the repeat. A row of sandbars on a gently sloping seabed is the same arrangement for ocean waves, and it does the same thing. Waves twice as long as the bar spacing are sent back out to sea, one small reflection per bar, all adding in step. A patch of eight bars can return most of the swell that meets it. The reflected wave, added to the incoming one, makes a standing pattern whose nodes are spaced exactly like the bars. Sand gathers in that pattern, so a field of bars can build its own next bar.

waves · Periodic media The chirp a staircase returns. The pitch of the echo of a clap from the staircase, heard by a listener 10 m from its foot, against time since the clap: the strongest frequency in successive 24 ms slices of the synthesised echo (dots), and the rate at which the reflections arrive, together with twice that rate (lines). The fundamental falls from about 767 Hz to 476 Hz over a sixth of a second, with its second harmonic an octave above — a descending chirp, which to many listeners sounds like a bird. It is Bragg reflection: the stair is a grating, the first-order echo is the frequency whose half-wavelength equals the extra path from one step to the next, and as the line of sight climbs, that extra path grows and the reflected pitch falls.

The chirp a staircase sings back

A hand clap at the foot of the great stair of El Castillo at Chichén Itzá is answered by a chirp — a falling whistle that some have compared to the call of the quetzal bird. Nothing in the stone is tuned. Each of the ninety-one steps returns its own copy of the clap, the copies arrive as a train of clicks, and the ear hears a regular train of clicks as a pitch. The pitch falls because the steps are not evenly spaced as the listener sees them: low steps are seen almost level, a tread apart, and high ones almost along the slope, a whole step's diagonal apart. It is Bragg reflection from a grating whose period, seen from one spot, changes along its length.

waves · Periodic media

Named alongside it

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

Band gapBloch waveChirpDiffraction gratingEchoPath differencePeriodic mediaPeriodic structurePitchRepetition pitchSediment transportShallow water waves

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