A pendulum wave is a phenomenon that occurs when a series of pendulums with slightly different lengths are set in motion at the same time. As they swing back and forth, they become synchronized in a wave-like pattern due to the principle of resonance. This happens because the pendulums are all moving at the same frequency or speed, which is called resonance. However, over time, small differences in the pendulum lengths cause the synchronization to break down and the motion becomes chaotic, exhibiting sensitivity to initial conditions and nonlinear behavior.