Combining waves at a point
When two waves occupy the same space, the displacement at any location is the sum of both wave amplitudes at that instant. This principle, called superposition, applies equally to sound waves in air, electromagnetic waves in light, and ripples on water. The result depends entirely on whether the waves are in sync or out of step with each other.
If the two waves crest at the same time, their amplitudes add directly, creating a larger wave; this is constructive interference. If one crests while the other troughs, they partially or fully cancel; this is destructive interference.
Phase relationships and interference patterns
The relative timing between two waves, called phase difference, determines whether interference is constructive or destructive. Waves separated by a full wavelength (0° phase difference) reinforce each other. Waves offset by half a wavelength (180° phase difference) cancel completely if their amplitudes are equal.
This principle explains why headphone noise cancellation works: it produces a sound wave precisely out of phase with ambient noise, allowing destructive interference to silence it. Optical experiments with light gratings and slits similarly produce bright and dark fringes where waves constructively and destructively interfere.