A wave is nothing more than a disturbance that moves from place to place in some medium, carrying energy with it. Since the behavior of waves is so closely related to the concept of oscillations, that is a good place to start.

There are many examples of simple oscillations, but a very good one is that of an object attached to the end of a spring. We will assume that the other end is held fixed, perhaps by a clamp. Suppose we let the spring hang vertically and slowly lower the object until it becomes stationary. The spring is now stretched enough for its upward pull to balance the weight of the object, which at that location is in equilibrium. Now we disturb the object by lifting it a short distance above that point and letting go. The object then begins to oscillate vertically as it...