## The Difference Between Standing Waves and Travelling Waves

Standing waves occur in confined spaces – in a microwave oven, on a violin string, They do not transport energy from one place to another because they are confined. The waves interfere as they move about within the space to set up a series of nodes, or points of minimum vibration, and antinodes or points of maximum vibration. The most striking feature of standing waves is that they only occur for certain frequencies – they display quantization, in the same way as energy is quantized for electrons in atoms, so that an electron may only have certain values, frequency is quantized for standing waves.

Consider a string fixed at one end. The free end is moved up and down. If an upward displaced pulse is introduced at the left end of the string, it will travel until it reaches the fixed end . Upon reaching the fixed end, the single pulse will reflect and undergo inversion. the upward displaced pulse will become a downward displaced pulse. If the free end is moved up at this point, an upward displacement will meet a downward displacement in the middle and the net effect will be zero displacement (destructive interference). If the free end is moved down at this point, a downward displacement will meet a downward displacement in the middle and the net effect will be a larger displacement (constructive interference). By varying the frequency so that the pulses are produced at certain intervals, there can be produced fixed points of destructive interference (nodes) and fixed points of constructive interference (antinodes). The waves keep bouncing backwards and forwards between the ends, but are confined to the string.

Travelling waves on the other hand actually move from place to place, transporting energy. Travelling waves can have any frequency, and can undergo interference just like standing waves. This interference is usually localized.

It must be realised that standing waves or travelling waves can move in one, two or three dimensions.

In one dimension a standing wave could be a vibration on a guitar string fixed at two ends. A travelling wave could be a light wave.

In two dimensions a standing wave could be a vibration on a drumskin. A travelling wave could be set up by a stone dropped into water. The stone sends out a circular wave pattern.

In three dimensions a standing wave could be set up by microwaves inside a microwave oven. A travelling wave could be set up by a bomb exploding in the open air.