When two or more waves interact (collide) with one another, at a given point, the resultant displacement is the algebraic sum of the displacements of the constituent waves.
Constructive and Destructive interference
If the two waves are completely out of phase with one another, they will cancel each other out completely, leaving nothing. This is known as destructive interference. If the two waves are 100% in phase with one another, then the resultant will be double the amplitude. This is known as constructive interference.