Our pendulum wave demonstrations (G1-82 and G1-83) are popular ways of showing wave phenomena. These demonstrations consist of a series of pendulums in a line, each with incrementally different periods. They are all started into motion at once, so their first swing is in phase, but then they move out of synchronization due to their slightly different periods. The differences in period were chosen such that the array of pendulums would themselves describe a wave, with a period related to the difference in periods of the pendulums. So over time they evolve a series of wave patterns as different pendulums move in and out of synchronization, before eventually briefly synching up again when they finally reach an integral multiple of all of their periods.
In a simulation, we can go beyond this, as removing the need for physical strings can enable even more complex wave patterns. Check out Don's latest animation below!