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Standing waves
Intermediate
Interference of opposite waves gives fixed nodes and antinodes.
standingTwo identical waves travelling in opposite directions form a pattern that doesn't move, with fixed nodes (zero amplitude) and antinodes (maximum). y = 2A sin(kx) cos(ωt).
A guitar string pinned at both ends.
Standing waves don't transport energy along.
In more detail
Standing waves form when two identical waves travel in opposite directions and superpose. They have fixed points of zero displacement called nodes and points of maximum displacement called antinodes.
Real-world uses
- Guitar strings vibrate in standing waves.
- Microwave ovens use standing waves in the cavity, which causes uneven heating.
- A guitar string plucked with fixed ends forms a standing wave, with a fixed frequency and a stationary pattern.
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Frequently asked questions
Do standing waves travel?
No. The pattern stays in place, although energy is confined between the nodes.
What is the spacing between nodes?
Half a wavelength.
Why do standing waves not move along the string?
Two waves of equal amplitude travelling in opposite directions interfere to give a pattern that does not travel.
Related topics in Waves & Sound
Constructive and destructive interference · Path difference and phase · Beats · Nodes and antinodes · Modes of a stretched string · Harmonics and overtones