Illustrated Physics
physics, drawn
Concept

Harmonic series — where it appears

The set of frequencies at whole-number multiples of a lowest one: one, two, three, four times the fundamental. A clamped uniform string and an open pipe sound it exactly, and any periodic signal is built from it, which is why a repeating waveform has a definite pitch.

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

Harmonics on a fixed string. Standing-wave patterns on a string clamped at both ends, at n = 1, 2, 3, 4. Only whole numbers of half-wavelengths fit, which is why the allowed frequencies are discrete.

Only some notes fit, and that is where discreteness comes from

A string clamped at both ends can vibrate at some frequencies and not others. A continuous object producing a whole-number list is the oldest quantisation in physics.

waves · Standing waves One turn of a circling charge, as it arrives. The radiation field reaching a distant observer in the plane of a charge's circular orbit, over one full turn, for speeds of 0.2c, 0.6c, 0.9c, each scaled to its own peak and plotted against arrival time as a fraction of the orbital period. At 0.2c the flash arrives 20.9 per cent of a turn wide at half height, having been emitted over 25.4 per cent; at 0.6c the flash arrives 6.0 per cent of a turn wide at half height, having been emitted over 14.2 per cent; at 0.9c the flash arrives 0.7 per cent of a turn wide at half height, having been emitted over 6.3 per cent. The slowest charge sends something close to a sine wave, with a trough 0.44 of its peak; the fastest sends a spike whose peak, divided by its speed, is 100 times a slow charge's, and a trough of 0.0028 of that peak. The field integrates to zero over every turn, as a radiation field must.

The flash a circling charge sends once a turn

A slow electron going round a magnet broadcasts one radio frequency. The same electron at nearly the speed of light, on a circle of the same kind, sends X-rays. Nothing about the mechanism changes between the two. The charge chases its own light, and the chase compresses one power of γ worth of emission into three.

astrophysics · Radiating charge

Named alongside it

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

Boundary conditionsCyclotronFourier transformLarmor formulaThe Lorentz factorNormal modesQuantisationRelativistic beamingRetardationStanding waveSuperpositionSynchrotron radiation

All concepts