Waves do not operate in isolation from each other, but can be added together.
When this addition causes the wave to grow we call this Constructive interference
When the addition of two or more waves causes the net (resultant) wave to be diminished we call this Destructive Interference.
Check out the Audacity files to make this happen
Here is a really good example of Interference in a web page.
http://www.kettering.edu/physics/drussell/Demos/superposition/superposition.html
youngs double slits experiment
https://www.youtube.com/watch?v=Iuv6hY6zsd0