Wave Interference and Beats

The superposition principle for waves may still seem a little mysterious. To avoid misconceptions, be aware that not all waves obey this principle! When you see two boats leaving wakes on a still lake, you can observe the wakes passing through each other to form interference patterns, just as the superposition principle predicts. But for a ship in stormy seas, the wake will be obliterated by the ocean's crashing waves, which is because waves of large amplitude usually fail to form superpositions. Waves obey the superposition principle only if the restoring forces in the medium obey Hooke's Law!

Hooke's Law is a proportionality between force and displacement that breaks down when the displacement from equilibrium is too large. A simple example of this breakdown is the pendulum we studied earlier. The component of the gravitational pull that acts to restore the pendulum to its vertical equilibrium ceases to be proportional to the angle with the vertical when that angle becomes too large. When we talk about wave interference, we assume that the wave amplitudes are small enough to make Hooke's Law valid. Watch this video, which summarizes the relationship between interference and beats.