Waves add up
Two billiard balls cannot occupy the same spot — they collide. Two waves can, and they simply add. The superposition principle says: where two waves overlap, the total displacement at each point is the sum of what each wave would give there alone. Add crest to crest and you get a taller crest; add crest to trough and they partly cancel.
Constructive and destructive interference
When two waves of the same frequency overlap steadily, the result is interference. If they arrive in phase — crest on crest — they reinforce into a bigger wave: constructive interference. If they arrive exactly out of phase — crest on trough, a half-wavelength offset — they cancel: destructive interference. Equal amplitudes can cancel to silence and darkness.
For two in-phase sources, the path difference Δr to a point decides the outcome; m = 0, 1, 2, …
The key idea is path difference. Two coherent sources send waves to a point by two routes; if one route is longer by a whole number of wavelengths, the waves arrive in step (constructive). If it is longer by a half-integer number of wavelengths, they arrive opposed (destructive). Sweep across space and you pass alternating loud and quiet — or bright and dark — bands.
Seeing the pattern
To see a stable pattern the sources must be coherent — the same frequency with a fixed phase relationship. Two independent loudspeakers wired to the same signal qualify; two random noises do not (their pattern would flicker and blur away). This same two-source geometry, done with light, is the famous double-slit experiment.