Stationary Waves
Simple Explanation
A stationary (or standing) wave forms when two identical waves travel in opposite directions and overlap β typically a wave and its own reflection. Unlike a travelling wave, a stationary wave does not move along the medium; instead, it has fixed points of zero displacement (nodes) and points of maximum displacement (antinodes) that stay in the same place.
Why Do We Need It?
Stationary waves are the basis of how musical instruments produce specific, stable notes β vibrating strings and air columns in pipes both work by setting up stationary waves.
Formula
Node Spacing in a Stationary Wave
distance between adjacent nodes = Ξ»/2
In a stationary (standing) wave, nodes (points of zero displacement) are evenly spaced, each separated by half a wavelength.
- Ξ»
- β Wavelength of the wave, in metres
When to use it: Use to find the wavelength of a stationary wave from the measured distance between two adjacent nodes (or antinodes).
Worked Example
Finding wavelength from node spacing
Adjacent nodes in a stationary wave are measured to be 0.3 m apart. Find the wavelength.
Why Does This Work?
When two identical waves travelling in opposite directions overlap, they interfere: at some fixed points, the waves are always exactly out of phase and cancel completely (nodes); at other fixed points, they are always exactly in phase and reinforce maximally (antinodes) β since this interference pattern doesn't move, the result appears to stand still.
Real-Life Example
A plucked guitar string
A plucked guitar string vibrates visibly, appearing to form a stable, blurred shape rather than a travelling wave.
The string's vibration is a stationary wave, formed by waves reflecting back and forth between the two fixed ends β the ends themselves are always nodes (zero displacement, since they're fixed), which is exactly why the string produces a stable, repeating pattern rather than a travelling wave.
Practice
Adjacent antinodes in a stationary wave are 0.15 m apart. Find the wavelength.
MediumCommon mistake
Confusing the distance between adjacent nodes with the full wavelength β adjacent nodes are only HALF a wavelength apart; a full wavelength spans from one node, past an antinode, to the SECOND node.
Quick Review
- Stationary waves form from two identical waves travelling in opposite directions (e.g. wave + reflection).
- Nodes: fixed points of zero displacement. Antinodes: fixed points of maximum displacement.
- Distance between adjacent nodes (or antinodes) = Ξ»/2.