Two pebbles strike the water at once, and keep striking. Every ripple from one crosses every ripple from the other. Where two crests arrive together the water leaps; where a crest arrives with a trough they cancel, and the water lies flat. Drag the pebbles. The stripes of calm will follow, and though every ripple races outward, the stripes themselves stand perfectly still.
For the curious kid.
Waves don't push each other out of the way: they pass straight through each other, and while they overlap, the water simply adds them up. Crest plus crest: double height. Crest plus trough: nothing at all. That "nothing" is the surprise. Between the two pebbles there are whole curved stripes where the two sets of ripples always arrive exactly out of step, so the water there never moves. Press long exposure to see what a slow camera would see: the racing ripples blur away and the standing stripes remain: bright where the waves agree, dark where they argue to a standstill. Now drag the pebbles apart and watch new stripes of silence be born.
Deeper.
The rule the water obeys is superposition: at every point, the total wave is the sum of the waves arriving there. A point hears each pebble after a delay set by its distance, so what matters is the path difference Δ = r₂ − r₁. If Δ is a whole number of wavelengths, the two arrivals march in step and reinforce. If Δ is an odd half-multiple (half a wavelength, one and a half, two and a half), they arrive exactly opposed and cancel. The set of points with a fixed |Δ| is a hyperbola with the two pebbles as its foci. Press the silent lines: those curves are drawn from that geometry alone, no simulation consulted, and they lie down precisely in the dark bands the water makes.
Two honest footnotes. Real ripples fade as they spread (this pool fades them as 1/√r, as energy conservation demands), so away from the middle the cancellation is deep but not total, and the true minima bend off the ideal hyperbolas by about two percent of a wavelength: the gold lines are the geometry, the water is the physics, and here the difference is thinner than a pixel. And real water disperses: ripples of different sizes travel at different speeds. Both pebbles here make the same wavelength, so the pool politely ignores it.
This picture is one of the most consequential in science. In 1801 Thomas Young sent light through two narrow slits (two pebbles, in effect) and saw these same stripes, which settled a century-old argument: light behaves as a wave, and the stripe spacing even told him its wavelength. A century later the stripes returned with a shock: electrons, fired at two slits one at a time, still build up the pattern, each electron somehow interfering with itself. Feynman called that a phenomenon "impossible, absolutely impossible, to explain in any classical way." And the argument between crest and trough is now an instrument: noise-cancelling headphones manufacture a trough for every incoming crest, and LIGO watched the silence between two laser beams tremble: the interference fringe that announced two black holes colliding a billion light-years away.
Where the waves agree, brightness. Where they argue, stillness. Most of what we know about light, atoms, and spacetime was read out of exactly that stillness.