Faraday waves explained

Shake a dish of liquid up and down and, above a certain strength, its surface suddenly breaks into a standing wave pattern. These are Faraday waves, first described by Michael Faraday in 1831.

Half the frequency

The surprising part is the timing. If the dish moves up and down 100 times a second, the waves rise and fall only 50 times a second: half the driving frequency. This is called a subharmonic response.

The reason is that shaking the dish does not push the waves directly. It changes the effective gravity the liquid feels, making it heavier and lighter in turn. A wave whose natural period is twice the shaking period gets a boost at just the right moment each cycle, like a child pumping a swing. Physicists describe this with the Mathieu equation; the effect is called parametric resonance.

A threshold

Below a certain shaking strength, the liquid's viscosity and the friction at the walls damp any wave out, and the surface stays flat. Above the threshold, a wave grows until nonlinear effects limit its height. Close to the threshold, a small change in loudness can make a pattern appear or vanish.

What decides the pattern

• Frequency. It sets the wavelength through the liquid's dispersion relation, which depends on gravity, surface tension and depth. Higher frequency means shorter waves and finer patterns.
• Container shape and size. Only waves that fit the container's walls can stand. A circular cell gives patterns built from Bessel functions: rings, and petals with a definite number of folds.
• Depth and liquid. Shallow water damps more and changes the wave speed. Viscous liquids need stronger shaking.
• Competition. When two modes are both near resonance, they compete, and the pattern can switch or mix between them.

In Aetheric Cymatics

Aetheric Cymatics models exactly this: a water cell shaken by sound, with the surface modes of the container, the Faraday threshold, damping and the optics of light reflecting off the surface. The Cell and Optics tabs let you change the container, depth and lighting and see how the pattern responds.