Illustrated Physics
physics, drawn
Concept

Frequency — where it appears

How many cycles a periodic process completes per unit time, and the quantity a clock counts rather than a duration it measures. It is the more fundamental of the two in practice, because counting is exact while measuring an interval is not — which is why the second is defined by a count of caesium cycles.

Named by 5 essays across 3 fields — each of them below, with the objects they name alongside it.

A travelling wave, caught at one instant. A sine wave plotted against position at a fixed moment. The wavelength is the distance between repeats. The ghosted curve is the same wave a moment later.

A wave is a shape that travels, and nothing else does

In a wave on water, no water goes anywhere. What moves is the shape — and separating the two motions is the whole of wave physics.

waves · Wave motion Wavefronts from a moving source. Circles showing where each crest has reached, centred on where the source was when it emitted them. Ahead of the source the crests are closer together and the frequency heard is higher; behind, they are spread out and it is lower.

The note that changes on approach, and the two ways of getting it

A moving source and a moving listener produce different formulas for the same shift, because the medium is watching. The difference is small, real, and the reason light had to be treated differently.

waves · Doppler 50 Hz on two strings: 5.66 m and 2.83 m. The same 50 hertz note driven onto 2 strings at the same tension of 80 newtons but different thicknesses. The frequency is identical — it is the source's — while the wavelengths are 5.66 metres and 2.83 metres, because each string carries the wave at its own speed.

The medium decides the speed, and the source only decides the note

A wave's speed is not chosen by whatever made it. It is a property of the material the wave is crossing, fixed before the wave arrives, and the wavelength is whatever is left over after the division.

waves · Wave motion The height a clock can see. The fractional difference in rate between two clocks against how far apart in height they are, on logarithmic axes — a straight line of slope one, since the shift is gh/c² and comes to 1.09e-16 per metre near the ground. a caesium fountain, good to 1e-16, resolves 91.6 cm; an optical lattice clock, good to 1e-18, resolves 0.9 cm; the best clocks built, good to 8e-19, resolves 0.7 cm. The caesium fountains that define the second reach about a metre. The optical clocks that will replace them reach a centimetre, and the best of them a few millimetres. That is the whole of why this has stopped being a test of relativity and become a way of measuring the ground. A shift once so small that it took a Mössbauer experiment in a tower to see at all is now large enough to be a nuisance: two clocks in the same building disagree, and the disagreement has to be corrected for before either can be used to keep time.

The clock that measures a height

A clock a metre higher runs faster by a part in ten thousand million million million. That was once so small it took a tower and a Mössbauer source to see; the best clocks now resolve a centimetre of height, at any distance, without a line of sight. What began as a test of general relativity has become a surveying instrument that measures the quantity surveying actually wants.

astrophysics · Gravitational redshift Where a speck lands decides how much it weighs. The fractional drop in frequency of a cantilever's first and second bending modes when a small mass lands on it, per unit of that mass as a fraction of the beam's, against where along the beam it lands, from the clamp to the free tip. The response is the square of the mode's displacement at the landing point divided by twice the mode's effective mass: a quarter of the beam for both modes (0.250 and 0.250), since each is measured against its own tip. At the tip both modes respond fully — the first by 2.0 times the landed fraction, the second by 2.0. Near the clamp neither responds, so a speck landing there is invisible. Halfway along, the first mode drops by 0.23 and the second by 1.02; at 0.783 of the length the second mode has a node and does not notice the speck at all. A single frequency cannot tell a light speck at the tip from a heavier one further in.

The weight a frequency can find

A spring's frequency is the square root of its stiffness over the mass it carries, so adding a little mass lowers the note by half the fraction added. Nothing in that rule cares about gravity, and nothing in it cares about size. It weighs astronauts in orbit by the swing of a chair, films a fraction of an atom thick on a quartz plate, and single molecules on a beam a few micrometres long — and it improves without limit as the thing that vibrates gets lighter. What it cannot do on its own is say where the added mass sat, and that turns out to matter as much as how much there was.

mechanics · Harmonic approximation

Named alongside it

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

Wave speedDispersionMeasurementWavefrontsWavelengthBoundary conditionsCalibrationCantileverClockDoppler effectEffective massEquivalence principle

All concepts