Sound

Faraday waves

Shake a dish of liquid at an audio frequency and standing waves rise on its surface: squares, hexagons, 8-, 10- and 12-fold quasi-patterns. The note sets the symmetry and the wavelength.

  • GPU shader
  • looping animation
  • works with sound
Open in the editor →

When a dish of liquid is shaken vertically at an audio frequency, its smooth surface freezes into ripples: a square grid, hexagonal cells, and at the right frequency eight- and twelve-fold patterns that never quite repeat. These are Faraday waves, the most striking pictures of cymatics.

How it works

Shaking does not push the liquid sideways; it makes gravity pulse. Each surface wave is then a pendulum with varying gravity, and it builds up most when swinging at half the pumping rate, like a child pumping a swing by standing and squatting twice per swing. So the ripples oscillate at half the drive frequency; their spacing follows the dispersion law, ruled in water at audio frequencies by surface tension.

ä + ω₀²·(1 + ε·cos Ωt)·a = 0 (Mathieu equation) main resonance: ω₀ = Ω / 2 water: ω² ≈ (σ/ρ)·k³, λ ∝ f^(−2/3) the layer: h = A(x)·cos ωt + 0.45·B(x)·sin ωt A = Σⱼ cos(k·(x · eⱼ)), eⱼ spaced 180°/N B — the same sum turned by 90°/N

A 100 Hz drive gives water waves about 6 mm long, 440 Hz about 2 mm. The generator adds up N standing plane waves: two make squares, three hexagons, four, five and six quasi-patterns with 8-, 10- and 12-fold symmetry. “Symmetry” “auto” follows the pitch: 55 Hz gives 4, 110 Hz 6, 220 Hz 8, and so on up to 16. The wavelength shrinks more gently than in water, as 1/√f, so the whole keyboard fits the dish. A second, rotated copy takes over as the first passes through zero, so the surface is never flat. As in cymatics photographs, a ring of lamps reflected in the slopes draws bright contours.

A bit of history

Michael Faraday described the ripples in 1831, noting that they oscillate at half the rate of the shaking. T. Brooke Benjamin and Fritz Ursell explained the effect in 1954 as a Mathieu instability. In 1967 the Swiss physician Hans Jenny named such experiments cymatics, from the Greek for “wave”. In the early 1990s experiments produced 8- and 12-fold quasi-patterns, liquid relatives of quasicrystals.

What to tweak

  • Step “Notes” by octaves: A1 squares, A2 hexagons, A3 eight-fold, A4 ten-fold, A5 twelve-fold.
  • “Light” “ring of lamps” with “Colour” “by slope direction” draws rainbow contours; “by height” gives a relief map.
  • More “Wave height”, more lines of light; “Meniscus” near 1 sends rings in from the wall.
  • Modulate “Wave height” with sound (source “sound”, band “bass”) and the dish trembles to a track or the microphone. A song arrives from the Studio via “Visualise in Patterns”, a video with sound (“Download” → “Video” → “With sound”) keeps the dance, and “Glow” makes the highlights shine.

Parameters

Notes
A note, a chord or a frequency: higher means more rays and shorter waves (wavelength ∝ 1/√f)
Symmetry
The rotational order of the pattern; “auto” follows the pitch auto · 4 · 6 · 8 · 10 · 12 · 14 · 16
Wavelength
Wave height
Steeper slopes draw more lines of light
Dish size
Meniscus
Rings rippling in from the wall of the dish
Light
ring of lamps · studio · by height
Colour
by slope direction · by height · one ink
Liquid colour
Oscillations per loop
The surface breathes and the pattern flows between its two sub-lattices; a chord is walked through once per loop