Faraday first described these waves in an appendix to an 1831 paper in the Philosophical Transactions. Drive a shallow layer of liquid vertically and, above a threshold amplitude, the flat surface goes unstable and a standing pattern appears — oscillating at half the driving frequency. That is parametric instability, and it is the reason the ripple you photograph is not beating at the tone you think you are playing.
The article is short but well chosen in its examples: ripples in a ringing wine glass, the fountain that climbs out of a singing bowl, and male alligators vibrating their lungs hard enough to throw Faraday waves off their backs during mating displays.
Applications listed include dynamic templates for assembling microscale materials, acoustic mixing and biological patterning — the respectable end of what a vibrating dish of liquid is good for.