Superposition and Stationary Waves
Two waves crossing add displacement to displacement, and a wave meeting its own reflection makes a pattern that does not travel. Nodes never move, antinodes swing hardest, and neighbouring nodes sit half a wavelength apart.
What a learner can do afterwards
- Applies the superposition principle to two pulses meeting, including the case where they cancel
- Marks nodes and antinodes on the first three harmonics of a string and gives each wavelength
- Finds the frequency of a harmonic from the length of the string and the wave speed
1 · Read
Crossing waves add displacement to displacement. Crests on crests build double height, while a crest on a trough cancels out.
Two identical pulses meeting crest to trough vanish for an instant, then pass through each other unchanged. A wave meeting its own reflection does this repeatedly, locking into a pattern that does not travel.
In that locked pattern, nodes never move and antinodes swing hardest halfway between nodes. Neighbouring nodes sit half a wavelength apart. On a string the first harmonic holds half a wave, the second one full wave, and the third one and a half.
Find a harmonic frequency from the string length and the wave speed. On a 1.2 m string the second harmonic spans one full wavelength of 1.2 m, so divide the speed by 1.2.
Adding waves builds standing patterns whose nodes split the string into half waves.
2 · Watch
Take it off screen
Where it sits
Learn first
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.