Illustrated Physics
physics, drawn
Concept

Capillary wave — where it appears

A ripple on a liquid surface short enough that surface tension, rather than gravity, provides its restoring force. Below a wavelength of about 1.7 cm on water such waves travel faster the shorter they are, their frequency growing as the 3/2 power of the wavenumber.

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

Which waves a moving object can make. The phase speed of waves on deep water against wavelength (red), with horizontal lines at the speeds of an object moving steadily across the surface: 15.0 cm/s, 23.1 cm/s, 30.0 cm/s, 50.0 cm/s. A steady object can only feed waves that keep pace with it, whose phase speed equals its own, and those are where its line meets the curve. At 15 cm/s the line misses the curve entirely: no wave can keep up, and the object leaves no wake. At 23.1 cm/s it touches the curve once. Above that it meets it twice: at 30 cm/s a ripple of 5.6 mm and a gravity wave of 5.2 cm; at 50 cm/s a ripple of 1.9 mm and a gravity wave of 15.8 cm.

The speed below which nothing on water leaves a wake

Every wave on clean water travels at 23 centimetres a second or faster: long waves are fast because gravity drives them, short ones because surface tension does, and in between there is a slowest wave. A boat, a duck or a fishing line can only make waves that keep pace with it, so anything crossing the water more slowly than 23 centimetres a second makes no waves at all. Faster, it makes two kinds at once — short ripples that run ahead of it and long waves that trail behind — and the threshold between nothing and both is set by gravity, surface tension and density alone.

waves · Wave motion Where shaking makes the surface unstable. For water 1 cm deep shaken vertically at 50 Hz, the regions of wavenumber and shaking acceleration in which a surface wave grows rather than decays, computed mode by mode from the Floquet multipliers of its damped Mathieu equation (inside the curves, unstable). The largest tongue reaches down to 0.80 m/s² — 0.081 g — at k = 633 m⁻¹, the wave whose own frequency is exactly half the drive's: a wavelength of 9.9 mm. A second, narrower tongue sits at k = 1066 m⁻¹, where the wave's frequency equals the drive's, and needs much harder shaking. Without damping both tongues would reach down to zero; viscosity lifts their tips, most for the shortest waves.

The ripples that answer at half the shaking

Shake a dish of water up and down fifty times a second and nothing happens — until the shaking passes a threshold, when the whole surface erupts into a pattern of standing ripples, squares or stripes, each crest rising and falling twenty-five times a second, at exactly half the frequency of the shaking. Michael Faraday saw it in 1831. The size of the ripples is not set by the dish. It is chosen by the water itself, as the one wavelength whose natural frequency is half the drive's, and the threshold is set by how quickly the water's own viscosity would kill that wave.

waves · Standing waves

Named alongside it

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

Critical velocityDispersionDispersion relationFaraday wavesGravity waveGroup velocityMathieu equationParametric resonancePattern formationPhase velocityStanding waveSurface tension

All concepts