---
title: "Superposition and Stationary Waves"
description: "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 h"
canonical: https://lightmysky.com/learn/science/superposition-and-stationary-waves-mt_AIxA2TYGJN
source: https://lightmysky.com/learn/science/superposition-and-stationary-waves-mt_AIxA2TYGJN.md
retrieved: 2026-09-12
---

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# 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.

Subject: Science · Area: Waves, Light & Sound · Ages 16 to 18
Page: https://lightmysky.com/learn/science/superposition-and-stationary-waves-mt_AIxA2TYGJN

## Ready when they can

- 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

## Lesson: Waves that add up and stand still

Crossing waves add displacement to displacement. Crests on crests build double height, while a crest on a trough cancels out.

**Example.** 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.

**Tip.** 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.

**Recap.** Adding waves builds standing patterns whose nodes split the string into half waves.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Polarisation as Evidence for Transverse Waves](https://lightmysky.com/learn/science/polarisation-as-evidence-for-transverse-waves-mt_mCbxv77qDA)
- [Progressive Waves: Phase and Path Difference](https://lightmysky.com/learn/science/progressive-waves-phase-and-path-difference-mt_RotpycCNF8)

## Opens up

- [Normal Modes of a Bounded System](https://lightmysky.com/learn/science/normal-modes-of-a-bounded-system-mt_650O-YrqJs)
- [Coherence and Young's Double-Slit Fringes](https://lightmysky.com/learn/science/coherence-and-youngs-double-slit-fringes-mt_mONvXhPmwq)
- [The Particle in a Box: Where Quantised Levels Come From](https://lightmysky.com/learn/science/the-particle-in-a-box-where-quantised-levels-come-from-mt_rOCXlEi324)
- [Huygens's Principle and the Laws of Reflection and Refraction](https://lightmysky.com/learn/science/huygenss-principle-and-the-laws-of-reflection-and-refraction-mt_xxdniF2__w)