Standing waves
A standing wave forms when two identical waves travel in opposite directions and interfere, producing fixed points of no displacement, called nodes, that never move.
Practise this conceptA standing wave forms when two identical waves travel through the same medium in opposite directions and interfere — the classic way to get this is a wave reflecting off a fixed end and running back into itself. Instead of a pattern that travels, you get one that stays put, oscillating in place.
Certain points, called nodes, stay completely still no matter how large the wave's amplitude is elsewhere, because the two opposing waves always cancel exactly there. Halfway between adjacent nodes sit antinodes, where the two waves always reinforce each other and the oscillation is largest.
Because a standing wave doesn't travel anywhere, it doesn't transport energy along its length the way a travelling wave does — the energy stays trapped, sloshing back and forth between the nodes. This is exactly the pattern behind musical instruments: a guitar string or an organ pipe rings at specific frequencies because only certain wavelengths fit neatly between its fixed ends to form a standing wave at all.
Key ideas
Requires: Interference and diffraction, Simple harmonic motion
Formulas
| Symbol | Name | Unit |
|---|---|---|
| frequency | Hz (hertz) | |
| speed | m/s (metre per second) | |
| distance | m (metre) |
Common misconceptions
- Every point on a standing wave has the same amplitude of oscillation.
- A standing wave transports energy along its length, just like a travelling wave.
- Nodes in a standing wave are points of maximum displacement.