Superposition
Definition
When two or more waves meet, their displacements simply add up — crest on crest makes a bigger crest; crest on trough can cancel out.
Technical definition
The principle that the net displacement at any point is the vector sum of the individual wave displacements. It underlies interference, standing waves, and beats, and holds for all linear wave systems.
Example
Noise-canceling headphones listen to incoming sound and broadcast its exact opposite — crest meets trough, the waves superpose to near silence, and the cabin roar disappears. Remove the headphones and the original sound is still there, untouched.
Superposition does not destroy the waves. After two pulses cross on a rope, each continues on its way unchanged — they only added up while overlapping. Students sometimes think canceling waves 'use each other up,' but interference is a meeting, not a collision; the energy reappears as the waves separate.