Throughout the rest of the course, we have focused on adding together two physical quantities that combine in fundamentally different ways.  We have calculated the total energy of a system by adding together terms that add as scalars.  Adding together energy terms is just adding together numbers.  We have also calculated the net force acting on an object by adding together forces.  Because forces are vectors, we needed to keep track of not just the magnitude of the forces but also their direction as we added them.  This module focuses on the third type of object that we need to add together, but that has its own rules for how we need to do it.  As two waves pass through each other, they create a resultant wave that we can calculate by adding together the two waves at each point where they overlap.  But like vectors, we need to keep track of two quantities when we add waves together, the amplitude of each wave and their phase difference.  Similar to the idea that we need to pay attention to magnitude and direction when we add together forces, we need to pay attention to amplitude and phase when we add together waves.

The relative difference between the phase of two waves will tell us how the waves interfere with each other.  When two waves line up perfectly, so that the peaks of the waves line up with each other, they interfere constructively.  Two waves can also line up so that the peaks of one wave line up with the troughs of another, they interfere destructively.  If two waves don’t interfere constructively or destructively, they exhibit intermediate interference.