The Principle of Superposition
What is a standing wave?
The example used above showed what happened when two single waves going in opposite directions met. A continuous wave is a set of single waves, one after another. You can produce such a wave by shaking one end of a rope up and down at a constant frequency. Now, if the other end of the rope is tied to something that doesn’t move, the wave will be reflected back toward you. If you shake the rope at the correct frequencies the two waves will overlap each other and will seem to stand still, producing a standing wave. Two distinct regions on a standing wave can be seen. At certain points the rope won’t be moving. That point is called a node. The point where the motion of the rope is largest is called the anti-node.
The nodes are locations of destructive interference where the two waves moving in opposite directions have opposite amplitudes; the crest of one wave and the trough of the other are at the same location. The anti-nodes are at locations of constructive interference where the two waves have both positive or negative amplitudes; that is, both are either crests or troughs.
The frequencies that produce standing waves depend on the length of the rope and the velocity of the wave on the rope. The lowest frequency will have nodes at the two ends and an anti-node in the center. The next higher frequency will have a node in the center and ends and two anti-nodes. At each higher frequency the number of nodes and anti-nodes increases by one.