C.4.1—Standing wave formation

Core idea

A standing wave forms when two waves with the same frequency, wavelength and amplitude travel in opposite directions and superpose. In practice, one wave is often the incident wave and the other is its reflection. The pattern oscillates in place rather than travelling along the medium.

Build the physical model

At each point, add the displacements of the two waves. Where they always cancel, the amplitude is zero: these fixed positions are nodes. Where they reinforce most strongly, the amplitude is greatest: these fixed positions are antinodes. The wave pattern repeats every half-wavelength, so adjacent nodes and adjacent antinodes are separated by $\lambda/2$, while a node and its nearest antinode are $\lambda/4$ apart.

Interpret what is and is not moving

The particles of the medium still oscillate between nodes and antinodes, but the locations of the nodes and antinodes do not move. A standing wave does not transfer energy progressively from one end to the other in the way a travelling wave does; energy is stored and exchanged locally within each segment between adjacent nodes.

Check the boundary

Do not describe a standing wave as a single wave travelling forward. First identify the two counter-propagating waves and then use superposition to explain the fixed pattern. The model here is limited to two identical opposite-travelling waves; the syllabus does not require superposition of more than two waves.