Standing Waves

When two progressive waves of the same frequency and amplitude travel in opposite directions through the same medium, they superpose to produce a very distinctive pattern called a standing wave (or stationary wave). Unlike progressive waves, standing waves do not transfer energy — they store it. Understanding standing waves is essential for explaining musical instruments, resonance, and for experimentally measuring the speed of sound.

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Formation of Standing Waves

A standing wave forms when a wave reflects from a boundary and the reflected wave meets the incoming wave. Both waves have the same frequency, wavelength, and amplitude but travel in opposite directions. The superposition of these two waves produces a pattern with fixed positions of zero displacement and fixed positions of maximum displacement.

On a stretched string fixed at both ends, a progressive wave travels along the string, reflects at the far end, and the reflected wave travels back. The incident and reflected waves superpose to create a standing wave.

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Nodes and Antinodes

Nodes are points on a standing wave where the displacement is always zero. At a node, the two progressive waves always cancel each other out completely (destructive interference at all times).