When two moving objects run into each other, they rebound (well, one of them at least). When two waves meet, they pass through each other. This is because waves do not collide. They superpose.
When the superposition results in a larger wave, (e.g. when two positive pulses superpose), we have a constructive interference.
When the superposition results in a smaller wave, (e.g. when a positive pulse superposes with a negative pulse), we have a destructive interference.
The outcome of a superposition is governed by the Principle of Superposition, which states that when waves overlap, the resultant wave’s displacement (at any position and time) is equal to the summation of all the overlapping waves’ displacement (at that position and time).
See the example on the following page. The blue pulse (travelling rightward) meets the red pulse (travelling leftward). Both pulses travel at 1 square per unit time. The resultant pulse (at each time unit) is shown in magenta on the right.
Constructive and Destructive Interference (Adam Neat)
Frame-by-Frame Superposition of Two Pulses