Stationary waves

​​In a nutshell

A stationary wave is formed when two progressive waves travelling in opposite directions with the same frequency superpose. A node is a point which always has zero displacement. An antinode is a point which always has the maximum displacement. 

Formation of stationary waves

A stationary wave is formed when two progressive waves travelling in opposite directions with the same frequency superpose. Ideally the amplitudes of the waves should also be the same.

When the waves superpose, there will be points at which they are antiphase. At these points their displacements will cancel and they form a point which always has zero displacement (amplitude). This is called a node.

There are also points where the waves are in phase. At these points their displacements will add together and form a point which always has the maximum displacement. This is called the antinode.

1. Node 2. Antinode

The antinodes oscillate between the positive largest amplitude and the negative largest amplitude. The node doesn't oscillate at all.

The separation between two adjacent antinodes is equal to half the wavelength of the original progressive waves. This is the same as the separation between two adjacent nodes. The frequency of the stationary wave is the same as the original progressive waves' frequency.

A stationary wave has no net energy transfer.

Example

Musical instruments use stationary waves to produce music notes. For example, a guitar forms stationary waves when the string is held down at each position.

Graphical representation of stationary waves

A stationary wave can be represented at different times using displacement-time graphs. The wave profile (snapshot of what the wave looks like) changes during the wave's cycle. This depends on the relative position of the two original progressive waves.

Note: In this diagram, the green line represents the resultant wave form and the red line represents when the blue and orange wave are completely in phase and overlap.

Each particle on the stationary wave between two adjacent nodes reaches its own maximum positive displacement at the same time. This means that all these particles are in phase, despite having differing maximum positive displacements.

These particles are antiphase with the particles on the other side of the node. This is because they reach their maximum positive displacement at the same time the other particles reach their maximum negative displacement.

Stationary waves and progressive waves

Stationary waves have different properties to progressive waves.