Wave Energy



Tie one end of a long piece of rope to a pole. Hold the other end in your hand. Pull the rope horizontal. Shake up and down quickly.

A wave starts from your hand and travels along the rope. Further down the rope, there is no wave. The wave has not reached there yet. It will, after a short time. This wave also carries energy, which travels with the wave.

The shape of the wave obviously travels from along the rope. We can see this in the moving crests. Where is the energy hidden?

Think of a short segment on the wave. As the wave passes over it, the segment moves up and down. So it has kinetic energy. If it oscillates, it must be because there is a force that keeps pulling it back to the rest position at the centre. The force must come from the rope on either side of the segment. When the segment moves up, the parts of the rope on the two sides are stretched. It is this tension that that tries to pull the segment back. So where there is wave motion, there is also elastic potential energy stored in the rope .

In this way, the motion of the segment is like the motion of a piece of wood attached to a spring. It is in simple harmonic motion. There is kinetic energy and potential energy. At the highest or lowest point, the segment is instantaneously at rest. There the kinetic energy is zero. The rope is most stretched, so the potential energy is largest. When the segment passes through the rest position, it at its fastest. Its kinetic energy is largest there. The rope is not stretched (compared to a rope at rest). So potential energy is zero.

From the conservation of energy, the total kinetic and potential energy of the segment must be constant, once it is moving up and down steadily. When the segment is at its highest, it is all potential energy. So this must be the same as the total energy. We know from spring motion that the potential energy is kx²/2. k is the spring constant and x is the displacement of a piece of mass attached to the spring. In the wave, the rope takes the place of the spring. The same formula applies. So the total energy of the segment is related to x² when x is at a maximum - that is, when x is the amplitude.

Thus, each bit of the wave has an energy that is proportional to the square of the amplitude. As the wave reaches further along the rope, it also carries this energy along.

A wave like this, in which both motion and energy travel from one place to another, is called a progressive wave.

There is another type of wave called stationary wave, in which motion and energy both stay at the same place. I shall talk about this later.


Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 23 May 2011.