What is the principle of a stationary wave?

The principle of a stationary wave is that it results from the superposition of two waves of equal frequency and amplitude travelling in opposite directions.

In more detail, a stationary wave, also known as a standing wave, is a wave that remains in a constant position. This phenomenon occurs when two waves of the same frequency and amplitude interfere with each other, travelling in opposite directions. The principle of superposition states that when two or more waves overlap, the resultant wave is the vector sum of the individual waves. In the case of stationary waves, this superposition leads to areas of constructive and destructive interference.

Constructive interference occurs at points where the two waves are in phase with each other, meaning they reach their maximum and minimum values at the same time. These points, known as antinodes, are where the amplitude of the stationary wave is at its maximum. On the other hand, destructive interference occurs where the two waves are out of phase, reaching their maximum and minimum values at different times. These points, known as nodes, are where the amplitude of the stationary wave is zero.

The unique characteristic of stationary waves is that they do not appear to move, or propagate, in space. This is in contrast to progressive waves, which transfer energy from one place to another. Instead, the energy in a stationary wave is confined to the space between the nodes. This principle is fundamental in many areas of physics, including acoustics and quantum mechanics. For example, the vibrations of a guitar string or the oscillations in a microwave cavity can be described as stationary waves.

In summary, the principle of a stationary wave is based on the superposition of two waves of equal frequency and amplitude travelling in opposite directions. This results in a wave that remains in a constant position, with areas of constructive and destructive interference creating a pattern of nodes and antinodes.