When we think of resonance, we often think of it in simple terms: hit the one right note, and the wine glass will shatter. But resonance isn’t always about a one-to-one ratio between a driving frequency and the resonating system. Especially in fluid dynamics, we often see responses that occur at other, related frequencies.
One of the simplest places to see this is with a droplet bouncing on a bath of fluid. Above you see a liquid metal droplet bouncing on a bath of the same metal. At low amplitude, the pool surface moves at the driving frequency and a droplet bounces simply upon that surface, with one bounce per oscillation. Increase the amplitude, though, and the droplet’s bounce changes. It bounces twice – one large bounce and one small bounce – in the time it takes for the pool surface to go through one cycle. This is called period doubling because the bouncing occurs at twice the driving frequency.
Turn the amplitude up further, and the system undergoes another change. Faraday waves form on the surface. They resonate at half the driving frequency, and a droplet’s bouncing will sync up with the waves. That means the droplet returns to a one-to-one bounce with the waves, but the waves themselves are no longer reacting at the driving frequency. It’s this kind of complexity that makes fluid systems fertile grounds for studying paths toward chaos. (Image and research credit: X. Zhao et al.)