1.6: Superposition and Interference
When two or more waves travel through the same medium at the same time, the waves pass through each other without being disturbed. The net disturbance or displacement of the medium is simply the sum of the individual wave displacements. This is true of waves that are finite in length (wave pulses) or continuous sine waves.
When the crests and troughs of the two waves are precisely aligned, the superposition produces pure constructive interference. Pure constructive interference produces a wave that has twice the amplitude of the individual waves but has the same wavelength.
On the other hand, destructive interference occurs when two identical waves arrive at the same point and are exactly out of phase (aligned crest to trough). Because the disturbances are in the opposite direction for this superposition, the amplitude is zero for pure destructive interference: the waves completely cancel each other out.
Read this text to learn more about standing waves and musical beats and see an interactive demonstration of wave interference on a water surface.
Watch this video to see how constructive and destructive interference is created by adding two waves while taking the sign of the wave's displacement into account at every point.
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.