Define and explain nodes and antinodes in standing waves.

Nodes are points of zero amplitude in a standing wave, while antinodes are points of maximum amplitude.

In a standing wave, the pattern of the wave appears to be stationary, but it is actually the result of two waves of the same frequency and amplitude travelling in opposite directions. This creates points along the wave where the two waves always interfere destructively, resulting in no movement. These points are called nodes. In contrast, there are points where the two waves always interfere constructively, resulting in maximum movement. These points are known as antinodes.

Nodes are characterised by a complete lack of movement. They occur at points where the two waves are always out of phase, meaning the crest of one wave coincides with the trough of the other. This results in destructive interference, where the two waves cancel each other out. As a result, the medium at a node does not move at all. In a string, for example, the nodes would be the points where the string does not move.

Antinodes, on the other hand, are characterised by maximum movement. They occur at points where the two waves are always in phase, meaning the crest of one wave coincides with the crest of the other, and the trough of one wave coincides with the trough of the other. This results in constructive interference, where the two waves reinforce each other. As a result, the medium at an antinode moves with maximum amplitude. In a string, the antinodes would be the points where the string moves the most.

The positions of nodes and antinodes are determined by the wavelength of the waves and the length of the medium. For example, in a string fixed at both ends, there will always be nodes at the ends of the string, and the distance between nodes (or antinodes) will be half the wavelength of the waves. Understanding the concept of nodes and antinodes is crucial for understanding the behaviour of standing waves, which are important in many areas of physics, including acoustics and quantum mechanics.