Standing Waves

Standing Waves

nodes and antinodes

Two waves travelling opposite ways add to a pattern that stays in place, with motionless nodes and big-swinging antinodes.

Example

Two waves travelling opposite ways add to a pattern that stays in place, with motionless nodes and big-swinging antinodes.

highlighted = computed this step

Two waves going opposite ways

Send identical waves along a string in opposite directions and they overlap everywhere. At some points the two always cancel; at others they always add. The combined pattern no longer travels — it just swings up and down in place. That is a standing wave.

opposite travelling waves  →  a pattern that stands\text{opposite travelling waves} \;\to\; \text{a pattern that stands}
A standing-wave patternA standing wave on a string with fixed points (open rings) that never move and bulges between them.

Nodes stay still; antinodes swing most

The points that never move are nodes; they sit half a wavelength apart. Halfway between each pair, the antinodes swing with the biggest amplitude. Because identical opposite waves cancel exactly at the nodes, the nodes are pinned in place.

node spacing=λ2\text{node spacing} = \tfrac{\lambda}{2}
Nodes (open rings) and antinodes (bulges)The standing wave with its motionless nodes marked as open rings and the swinging antinodes bulging between them.
waves Nodes sit exactly a half wavelength apart, marked as open rings where the waves always cancel.