When two waves — sound, light, water, or any other kind — meet and overlap in the same region of space, they don't collide or deflect off each other the way two physical objects would. Instead, the principle of superposition holds that their individual displacements simply add together at every overlapping point, producing a single combined wave whose displacement at each point is just the sum of what each individual wave would have produced there on its own. Depending on exactly how the two waves' peaks and troughs line up at a given point, that simple addition can either reinforce them into something larger, or cancel them out into something close to nothing at all.
Constructive interference happens when peaks meet peaks
When two waves arrive at a given point with their peaks and troughs aligned — a state called being in phase — their displacements add together constructively, producing a combined wave with a noticeably larger amplitude than either individual wave had on its own. This constructive interference is why, for instance, carefully arranged, synchronised speakers can produce a louder combined sound at certain points than either speaker could achieve alone, since the two sound waves' peaks are arriving together and reinforcing each other at those specific locations.
Destructive interference happens when a peak meets a trough
When two waves instead arrive at a given point with one wave's peak lining up against the other wave's trough — a state called being out of phase — their displacements largely cancel each other out, producing a combined wave with a much smaller amplitude than either individual wave, and in the extreme case of two waves with identical amplitude perfectly out of phase, complete cancellation, meaning effectively silence or darkness at that exact point even though both original waves are still very much present and travelling through that same location. This destructive interference is precisely the underlying principle behind active noise-cancelling headphones, which generate a sound wave specifically timed to be out of phase with incoming ambient noise, deliberately engineering destructive interference to cancel out much of that unwanted sound before it ever reaches the wearer's ear.
What we're still unsure about
The principle of superposition, and the mechanics of constructive and destructive interference it produces, are precisely defined, thoroughly confirmed classical wave physics, verified across an enormous range of experiments with sound, light and other kinds of waves. What requires real, careful application rather than being conceptually unsettled is correctly predicting the specific interference pattern a genuinely complex real arrangement of multiple wave sources will actually produce across an entire extended space, rather than just at one single simple point — real interference patterns from multiple sources can be genuinely intricate, and correctly working out where constructive and destructive interference will occur across a full two- or three-dimensional space takes careful, deliberate calculation, not simply applying the basic peak-meets-peak or peak-meets-trough intuition to every point at once.
This sits inside Superposition & Interference, one of eight topics in Waves & Optics, one of five domains in Physics, one of seventeen subjects the app can quiz you on.