Stationary Waves

Objectives

Lesson outcomes

Explain how superposition of two waves travelling in opposite directions forms a stationary wave.
Identify nodes and antinodes on stationary-wave diagrams and in demonstrations.
Describe stationary-wave demonstrations using microwaves, stretched strings, and air columns.
Determine wavelength from the spacing of nodes or antinodes.

Syllabus

CIE 9702 syllabus points

4 linked

8.1.1 explain and use the principle of superposition
8.1.2 show an understanding of experiments that demonstrate stationary waves using microwaves, stretched strings and air columns (it will be assumed that end corrections are negligible; knowledge of the concept of end corrections is not required)
8.1.3 explain the formation of a stationary wave using a graphical method, and identify nodes and antinodes
8.1.4 understand how wavelength may be determined from the positions of nodes or antinodes of a stationary wave

Lesson Notes

Student guidance and lesson notes

Overview

Stationary waves form when progressive waves travelling in opposite directions superpose. The resulting pattern has fixed nodes and antinodes, which can be used to determine wavelength in strings, air columns, and microwave experiments.

What You Need to Know

A stationary wave can form when a wave and its reflection have the same frequency and similar amplitude and travel in opposite directions.
Nodes are points that remain at zero displacement.
Antinodes are points of maximum amplitude.
Adjacent nodes are separated by lambda / 2. Adjacent antinodes are also separated by lambda / 2.
A node and the nearest antinode are separated by lambda / 4.
Stationary waves can be demonstrated with microwaves, stretched strings, and air columns.
Unlike a progressive wave, a stationary-wave pattern does not transfer energy along the pattern.

How to Work Through It

Start by comparing a progressive wave with a stationary-wave pattern.
Use two opposite travelling waves to explain where nodes and antinodes form.
Interpret diagrams for strings, air columns, and microwave stationary waves.
Practise wavelength calculations from node-node, antinode-antinode, and node-antinode distances.

Check Your Understanding

What two waves superpose to form a stationary wave?
How far apart are adjacent nodes?
How can microwave detector readings be used to find wavelength?
Why is a stationary wave not the same as a wave that has stopped moving?

Common Mistakes

Calling every peak an antinode without considering the full oscillation pattern.
Using node-antinode spacing as a full wavelength.
Describing stationary waves as transferring energy from one end to the other like progressive waves.
Forgetting that the pattern is fixed but the particles still oscillate except at nodes.

Next Steps

Practise marking nodes and antinodes on different stationary-wave diagrams.
Prepare for revision by comparing progressive waves, interference patterns, and stationary waves.