Superposition

What happens when two waves arrive at the same place at the same time?
Imagine 2 coherent sources emit waves into the same space at the same time. What will happen when they meet?

In some places the two waves will add together. They will INTERFERE CONSTRUCTIVELY

In other places they will cancel each other out. They will INTERFERE DESTRUCTIVELY

Whether they do or not will depend on their phase difference.

If the waves arrive in phase then they will interfere constructively and there will be a maximum at that point. 
If the waves arrive in antiphase (1800 out of phase) then they will interfere destructively and there will be a minimum at that point.

They phase difference between the waves when they arrive at any point will depend on their "path difference". This is the difference in how far they have traveled.

The waves will arrive in phase if:

They have traveled the same distance (p.d. = 0)  or

Their path difference is a whole number of wavelengths i.e. p.d. = n

The waves will arrive in antiphase if:

Their paths differ by half a wavelength i.e. p.d. = n   + / 2