Pendulum Wave
Fifteen pendulums, released together, each swinging at its own steady rate and connected to nothing. Within seconds they form a travelling wave; at twenty seconds they sit in three groups, at thirty in two, and at sixty every one of them is back in line. Pull the row back and let go, pluck one out of step, or turn the sound on and listen to the pattern phase like a piece of minimalist music.
A row of pendulums hangs from one beam, each a little shorter than the one before. Pull them all back together and let go. For a moment they swing as one. Then the short ones pull ahead, the row bends into a snake, the snake tightens into waves, the waves break into two interleaved teams swinging in opposite directions, then three, then something that looks like noise. And then, a minute after you let go, every bob arrives at the same side at the same instant, as if nothing had happened.
The surprise is that nothing is happening between them. No spring, no shared string, no pendulum feels any other. Each one does the dullest thing a pendulum can do: swing at its own steady rate forever. The lengths are chosen so that in one cycle time the longest swings 51 times, the next 52, the next 53, and so on. Neighbours drift apart by one swing per cycle, so at a third of the cycle they are a third of a swing apart and the row falls into three groups; at half the cycle, half a swing apart, so alternate pendulums are on opposite sides. Every pattern you see is a beat between frequencies, and the whole show is arithmetic.
The version most people know comes from the Harvard Natural Sciences Lecture Demonstrations, and the physicist Richard Berg described the design for teachers in 1991. Here you can change the rules it is built on: more or fewer pendulums, a longer or shorter cycle, faster base swings, a bigger release. The phase wheel under the stage turns each pendulum into a dot on a clock face, so a straight spoke means in line, two opposite spokes mean two groups, and a spiral means a travelling wave.
Beats like these are everywhere a few close frequencies meet. Two guitar strings slightly out of tune throb at the difference of their pitches. Steve Reich's phasing pieces, such as Piano Phase, play one pattern against itself at a slightly different speed and let the listener hear the same drift this row shows. Turn the sound on: each bob strikes a marimba note at the end of its swing, so the moment of realignment is a chord.
Trace sunlight through a single raindrop and watch the rays pile up at one angle — then see that pile-up paint a double rainbow, a dark band, a fogbow and a rainbow in a garden hose.