Pond Ripples: How a Frog's Jump Becomes a Perfect Circle of Waves

A ripple is a circle that grows at a fixed speed

When a frog lands on a still pond, it pushes water down and the surface springs back, overshoots, and the disturbance spreads outward as a ring. That ring is a circular wave: every point the disturbance reaches starts oscillating up and down, and the ring's radius grows at the wave's speed, which for small ripples on shallow water depends mostly on gravity and the water depth, not on how hard the frog jumped.

A harder jump makes a bigger amplitude ripple — a taller, more visible ring — but it travels at essentially the same speed as a gentle one, the same way a loud clap and a quiet clap both travel through air at the speed of sound. Amplitude and speed are independent properties of a wave; only the medium (here, the water's depth and surface tension) sets the speed.

Interference: what happens when two ripples meet

When two frogs jump at once, their rings expand and pass through each other. At every point where two crests arrive together, the water rises higher than either ripple alone would make it — constructive interference. Where a crest meets a trough, they partly or fully cancel — destructive interference. This is the superposition principle: for small ripples, the total displacement is simply the sum of each wave's individual displacement, and after they cross, both ripples continue on exactly as if the other had never been there.

total height at a point  =  height from ripple 1  +  height from ripple 2

crest + crest  →  extra-tall bump   (constructive)
crest + trough →  flat / cancelled  (destructive)

Why ripples fade

As a ring expands, its energy is spread over an ever-longer circumference, so its height shrinks even before any energy is lost to friction — the same spreading-out effect that dims a light bulb with distance. On top of that, real water has viscosity and the ripple's own surface tension damps the smallest, fastest ripples first, which is why a pond settles back to stillness within a few seconds of a single frog's leap, while a slower, larger disturbance — a dropped stone, a swimming duck — can be seen for much longer.

Lily pads and reflection

A lily pad floating on the surface is a boundary: some of the ripple energy reflects off it, some bends around its edge (diffraction), and the pad itself bobs up and down as the wave passes beneath. Frogs use lily pads as launch and landing platforms, and the ripples a frog makes when it lands give nearby frogs — and predators — a cue about where it is, which is one reason a startled frog often dives for cover rather than staying still on an exposed pad.

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