Consider the harmonic, periodic wave below. The wave is moving from left to right, but the particles of the "string" are moving up and down.

Focus on a single colored particle in the string. The motion of an individual particle is a simple harmonic oscillation, which can be described by an equation of the form:

y(t) = A sin(wt + d)

All particles have the same amplitude A and same frequency w, but they all have different phases d.

Credits:

Modified from Andrew Duffy's web page at Boston University. The animation uses the Physlet Java Applets of Wolfgang Christian and Mario Belloni.