Wave interference
Interference is what happens when two or more waves meet and their effects add up. Depending on how their waves line up in time (their phase), the combined wave can be stronger (constructive interference) or weaker (destructive interference).
Key idea: superposition. When waves overlap, the at-a-point displacement is the sum of the individual displacements. If crests line up with crests, you get a larger amplitude. If a crest meets a trough, they partially or completely cancel.
This happens for all kinds of waves—light, sound, water waves, and even matter waves. In ideal media, energy is conserved: where interference cancels, energy is redistributed to other places.
Phase matters. Constructive interference occurs when the phase difference is an even multiple of π (0, 2π, 4π, …). Destructive interference occurs when the phase difference is an odd multiple of π (π, 3π, 5π, …). When the phase is in between, you get a result between the two extremes.
A simple everyday example is dropping two stones in a pond. Each stone creates circular waves; where the waves meet in phase, the water moves more; where they’re out of phase, the motion nearly vanishes. Far from the stones, you can see regular interference patterns as rings or lines.
Light interference is a famous case. We don’t usually observe the electric field of light directly, only its intensity, which is proportional to the square of the total wave. If two light beams of the same intensity meet in phase, their bright fringes can be much stronger; if they’re out of phase, dark fringes appear. Light must be coherent (stable in phase) to produce clear interference, which is why lasers are especially good for interference experiments.
A common setup is two waves crossing at an angle. The phase difference varies with position, creating a fringe pattern. The spacing of the bright fringes depends on the wavelength and the crossing angle. For two plane waves crossing at angle θ, the fringe spacing is roughly λ/sinθ. If you look at two distant point sources, you get a pattern of circular or near-straight fringes, depending on distance and viewing angle.
There are two main ways to produce and observe interference: amplitude division (split the light into two paths and recombine, as in the Michelson or Mach-Zehnder interferometers) and wavefront division (split the wavefront in space, as in Young’s double-slit setup). Interferometers are used to measure tiny distances very precisely and to calibrate length standards. Astronomy uses interferometry to combine signals from separate telescopes to achieve very high resolution.
Quantum interference works similarly with matter waves. If a particle’s possible paths interfere, the probability of finding the particle in a region includes a cross term that can boost or reduce the likelihood, just like waves. The classic example is the double-slit experiment with electrons, atoms, or molecules.
In acoustics, a related effect is beats: two tones with nearly the same frequency produce a fluctuating volume (the difference between the frequencies), which we hear as a beating sound.
In short, interference is the way waves combine when they meet. It explains bright and dark fringes, helps us measure tiny distances, and even reveals the wavelike nature of matter.
This page was last edited on 2 February 2026, at 12:05 (CET).