Cymatics: how sound makes patterns

Cymatics is the study of sound and vibration made visible. When a plate vibrates at one of its own pitches, it bends in a fixed pattern, and sand sprinkled on it is thrown off the moving parts and settles on the lines that stay still. Each pitch draws its own figure, and the figure depends on the plate's size, thickness and material as much as on the pitch.

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Grains of yellow sand settled into eight long, wavy parallel lines across a dark field, swelling gently in the middle — Illustration, drawn in code. Each grain of sand is carried to the nearest still line of a standing wave, as on a vibrating plate, in the yellow of 528 Hz; the lines follow the long waves of the Harmonance field rather than any one real plate.

What is cymatics?

Cymatics is the study of vibration made visible. A plate, a drum skin or a dish of water vibrates at one steady pitch, and a thin layer of sand, powder or liquid on top shows the shape of the vibration: where the surface moves, and where it stays still. The patterns are physics, and anyone with a speaker and a little salt can make them.

The word is modern. It comes from the Greek kyma, a wave, and was coined by Hans Jenny, a Swiss doctor and painter who spread powders, pastes and liquids on metal plates driven by an oscillator and published his studies in two volumes called Kymatik, in 1967 and 1972. The Historical Dictionary of Switzerland describes his field as the experimental making visible of wave and vibration phenomena. The figures themselves are much older: they carry the name of Ernst Chladni, who published them in 1787.

How does sound make patterns in sand?

A plate made to sound at one of its own pitches does not move as one piece. It bends into a standing wave: some regions rise while their neighbours fall, hundreds or thousands of times a second, and between them run lines that hardly move at all. Sand on the plate is bounced off the moving regions and comes to rest on those still lines, which physicists call nodal lines. Michael Faraday summed up the sand figures in 1831:

They indicate the quiescent parts of the plates, and visibly figure out what are called the nodal lines

A plate seen edge on, swinging between two curves with sand heaped where they cross, and the same plate from above with four lines of sand — Sand gathers where a vibrating plate stays still. Seen edge on, the plate swings between two curves that cross at two still points; seen from above, those points lie on the four still lines of figure 6 of a square plate.

The pattern is a map of stillness. At 528 Hz a plate bends one way and back 528 times a second, far too fast to see, but the sand keeps the record: wherever it piles up, the plate is not moving.

Very fine powder does something else. Faraday saw light dust gather in the middle of the moving regions instead, "towards those parts of the plates where the excursions are greatest", and showed why by vibrating a glass plate inside a jar with most of the air pumped out. There, fine silica "went from the middle towards the nodal line or place of rest, performing exactly the part of sand in air". The dust had been carried by small currents of air that the moving plate stirs up. Under water he saw the opposite of sand in air: brass filings formed lines that were "not however lines of rest, as they would have been in the air, but were the places of greatest vibration".

Who discovered cymatics?

Robert Hooke saw the first of these patterns in 1680, when he ran a bow along the edge of a glass plate covered with flour (Wikipedia, Cymatics). The musician and physicist Ernst Chladni made a study of them a century later. He held a metal plate fixed at its centre, drew a violin bow along an edge, and found that each pitch the plate gave out came with its own figure in the sand. He published his drawings in 1787 in Entdeckungen über die Theorie des Klanges, Discoveries on the theory of sound.

From the first sand figures to the word cymatics: the people who saw the patterns, explained them and named them.

Cymatics through time
Year	Who	What happened
1680	Robert Hooke	Sees patterns in flour on a bowed glass plate
1787	Ernst Chladni	Publishes the sand figures of bowed plates
1808	Napoleon	Sees them in Paris and sets a prize for their mathematics
1816	Sophie Germain	Wins the prize with the first theory of a bending plate
1831	Michael Faraday	Explains why fine powder moves unlike sand, and finds water rippling at half the plate's frequency
1850	Gustav Kirchhoff	Shows which equations the figures obey
1883	Lord Rayleigh	Confirms Faraday's half frequency
1909	Walther Ritz	Computes the figures of a square plate accurately for the first time
1967	Hans Jenny	Names the field: Kymatik, cymatics

Explaining the figures took far longer than drawing them. Napoleon watched Chladni demonstrate them in Paris in 1808 and set a prize for the best mathematical explanation. Sophie Germain won it on her third attempt, and in 1816 became the first woman to win a prize from the Paris Academy of Sciences, though her model of a bending plate still needed corrections. Gustav Kirchhoff found the right equations in 1850, and even then the square plate held out: Lord Rayleigh wrote in his treatise on sound that the problem of a rectangular plate with free edges was "one of great difficulty".

The first accurate figures for a square plate were computed in 1909 by Walther Ritz, who knew he was dying of consumption and invented a new method of approximation to do it (Gander and Kwok, 2012). Engineers took up his method straight away, and it is known today as the Galerkin method.

Why does each pitch draw a different figure?

A plate does not have one pitch. It has a long series of pitches at which it rings freely, and each comes with its own way of bending, so each draws its own figure. Chladni found them by ear, bowing at different points of the edge. Gander and Kwok, two mathematicians who recomputed his square plate in 2012, call his results "exceptionally accurate" for someone who "relied on his ear for the frequencies".

Higher pitches draw busier figures, with more still lines closer together, because the plate bends into more and smaller regions. Which pitches a plate has depends on its size, its thickness and what it is made of. For plates of the same glass and shape, every pitch rises in step with the thickness and falls with the square of the width: a plate twice as wide sounds each of its figures two octaves lower, and a plate twice as thick sounds them an octave higher.

Does 528 Hz make a special pattern?

No pitch has a pattern of its own. A Chladni figure belongs to a pitch and a plate together, so the same tone draws a different figure on each plate, or none at all. To show it, Harmonance computed where 528 Hz falls on four square plates of ordinary 2 mm window glass, using Ritz's method and Gander and Kwok's published values for a plate with free edges, and the stiffness and density of float glass from Pilkington's technical bulletin.

The figures of 15, 20, 25 and 30 cm glass plates as rows of ticks on a pitch axis, and a yellow 528 Hz line that sits near a tick in two rows only — On four square plates of 2 mm glass, 528 Hz lands 3.9 Hz from a figure on the 25 cm plate and 9.6 Hz from one on the 15 cm plate, but more than 70 Hz from any figure on the 20 and 30 cm plates.

The numbers behind the chart
Plate	Nearest figure	From 528 Hz
15 cm	Figure 3, 537.6 Hz	9.6 Hz above
20 cm	Figure 4, 455.6 Hz	72.4 Hz below
25 cm	Figure 6, 531.9 Hz	3.9 Hz above
30 cm	Figure 9, 608.2 Hz	80.2 Hz above

Download the plate pitches (CSV)

On the 25 cm plate, 528 Hz sits 3.9 Hz from the plate's sixth figure, the one drawn above: four still lines running parallel to the edges and bending out to meet them near the corners. On the 15 cm plate it sits 9.6 Hz from the third figure, a single still line in the shape of a rounded square. On the 20 and 30 cm plates it falls between two figures, more than 70 Hz from either, where the plate has no figure of its own to draw. Change the thickness, the glass or the way the plate is held, and every one of these pitches moves again.

So a picture shared as the pattern of 528 Hz shows one plate, or one dish of water, at that pitch. It is a real picture of real vibration, but it belongs to that plate as much as to the number. The 528 Hz guide follows where the number itself comes from, and what the claims made for it rest on.

How do patterns form in water?

Water on a vibrating plate makes patterns of its own, and they keep a different time. Faraday saw fine standing ripples, which he called crispations, on water over the moving regions of a plate, and found them "occurring in twice the time of the vibrations of the plate": the water rises and falls once for every two vibrations of the plate. Lord Rayleigh measured it again in 1883, with a bar kept vibrating by an electromagnet, and confirmed that "there are two complete vibrations of the support for each complete" vibration of the water (Rayleigh, 1883).

These ripples are now called Faraday waves. When a dish of water on a speaker shows them at 528 Hz, they rise and fall 264 times a second, at half the frequency of the sound that drives them.

What can cymatics not show?

Cymatics shows how a plate or a liquid moves. It cannot show what a sound does to a person. Pictures of figures are often shared beside claims about what a frequency does inside us, but a figure records one surface at one pitch, and the same pitch draws a different figure on the next plate. Nothing in the pattern carries over to someone listening.

Whether sound and music affect health is a separate question, answered by studies of people rather than plates. The US National Center for Complementary and Integrative Health sums up that research plainly: "because much of the research on music-based interventions is preliminary, few definite conclusions about their effects have been reached" (NCCIH, music and health). For what studies of sound do and do not show, read what the science of sound healing shows.

Can you try cymatics at home?

Yes, with a small speaker, a thin plate and some salt. University physics departments use the same set-up: in Simon Fraser University's lecture demonstration a metal plate sits on a driver fed by a signal generator, and "at specific frequencies, the salt accumulates at certain locations of the plate". Its kit list includes earmuffs and earplugs: a plate ringing at one of its own pitches can be loud.

Fix a thin, flat, square plate by its centre to a small speaker or driver: a bolt through the middle, or strong double-sided tape on the centre of the speaker.
Scatter a thin layer of dry, fine sand or table salt over the plate.
Play a steady tone from a tone generator, starting low in pitch and low in volume.
Raise the pitch slowly. The salt trembles and then, at certain pitches, runs into lines: those are the plate's own figures. Between them it only shivers.
Write down each pitch that draws a figure. Higher pitches draw busier figures.

A speaker pushes the plate at its centre, so it can only start figures whose centre moves. Of the first 15 figures of a free square plate, only four do: the third, sixth, eleventh and fifteenth, as the plate pitches download marks. Chladni's own way finds many of the rest: hold the plate firmly at its centre and draw a violin bow down one edge.

Keep the volume low, and stop if the plate starts to shriek. The World Health Organization's safe listening advice is that "you can safely listen to a sound level of 80dB for up to 40 hours a week", with a device's volume at no more than 60% of its maximum.

Is the Harmonance field cymatics?

No. The waves that move behind Harmonance's pages are an animation, drawn by code in the colour of the tone that is playing. They take two things from the sound: its pitch, so a higher tone draws shorter waves, and the loudness of what is actually playing, which the page measures as it plays and turns into the height of the swell. Nothing on the screen is a plate or a liquid, and the shapes are drawn for the eye rather than computed from physics.

The figures in this guide are the other way round: every still line in them is computed from the equations Ritz solved, for a plate of real glass. To hear the 528 Hz tone they are built around, press play above or open the 528 Hz page. The Solfeggio collection plays it beside the other eight Solfeggio tones, and nothing plays until you press play.

Sources and limits

The history rests on Chladni's 1787 book, Faraday's 1831 paper and Rayleigh's 1883 paper, each read in a scan of the original, on Gander and Kwok's 2012 account of the mathematics, and on encyclopaedia entries for Hooke, Napoleon's prize, Sophie Germain and Hans Jenny. The chart and the diagram are Harmonance's own computation, by Ritz's method for a square plate with every edge free, which matches Gander and Kwok's published values to within half of one per cent, with glass properties from a manufacturer's bulletin. A real plate is held or driven at some point, which shifts its pitches, so the numbers show the principle rather than a recipe for any one plate. No figure belongs to 528 Hz alone, and a pattern on a plate says nothing about health.