AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Nodes and antinodes on strings.
Full specification wording
Principle of superposition of waves and formation of stationary waves: Nodes and antinodes on strings.
When a string is fixed at both ends and driven at a suitable frequency, waves reflect at the boundaries and travel back through each other.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 2 of 7
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
When a string is fixed at both ends and driven at a suitable frequency, waves reflect at the boundaries and travel back through each other. Superposition of the two travelling waves produces a stationary wave: a pattern that stores energy rather than transporting it along the string. A node is a point of permanently zero displacement, where the two waves always cancel because they arrive in antiphase. An antinode is a point of maximum displacement, where the waves always reinforce because they arrive in phase. Adjacent nodes are separated by half a wavelength, and the same is true of adjacent antinodes. For a string of length L fixed at both ends, the ends must be nodes, so L = nλ/2 and the allowed wavelengths are λ = 2L/n, where n is a positive integer. The simplest pattern, n = 1, has one antinode at the centre.
What earns the marks
- A node is a point of zero displacement at all times, produced where the two travelling waves are always in antiphase and cancel by superposition.
- An antinode is a point of maximum displacement, produced where the two travelling waves are always in phase and reinforce by superposition.
- The distance between adjacent nodes, or between adjacent antinodes, is λ/2, so the distance from a node to the next antinode is λ/4.
- For a string fixed at both ends, the fixed ends must be nodes, giving L = nλ/2 and allowed wavelengths λ = 2L/n for n = 1, 2, 3, ...
- The amplitude of the stationary wave varies with position along the string, unlike a travelling wave, which has the same amplitude everywhere.
- Energy in a stationary wave is stored between the nodes rather than transferred along the string, because the two travelling waves carry energy in opposite directions.
Common mistakes and how to put them right
Treating a node as a point of minimum but non-zero displacement.
Put it right by stating that at a node the displacement is exactly zero at every instant.
Confusing the node-to-node distance with a full wavelength.
Put it right by using λ/2 between adjacent nodes and λ/4 between a node and the next antinode.
Assuming any driving frequency produces a stationary wave on a fixed string.
Put it right by requiring the wavelength to satisfy λ = 2L/n so that both fixed ends are nodes.
Exam tips
- Sketch the string pattern and label nodes and antinodes before writing any explanation, so your description matches the diagram.
- When asked to find a wavelength or frequency, first count the number of half-wavelengths that fit between the fixed ends.
- Use the phrase 'superposition of two waves travelling in opposite directions' to show you understand the mechanism, not just the pattern.
Try the lesson
The start of the Principle of superposition of waves and formation of stationary waves: Nodes and antinodes on strings. lesson, made from checked teaching notes for this specification point.
Have a go first
On a stationary wave on a string, what is the name of a point that does not move at all?
Listen
When a string is fixed at both ends and driven at a suitable frequency, waves reflect at the boundaries and travel back through each other. Superposition of the two travelling waves produces a stationary wave: a pattern that stores energy rather than transporting it along the string. A node is a point of permanently zero displacement, where the two waves always cancel because they arrive in antiphase. An antinode is a point of maximum displacement, where the waves always reinforce because they arrive in phase. Adjacent nodes are separated by half a wavelength, and the same is true of adjacent antinodes. For a string of length L fixed at both ends, the ends must be nodes, so L = nλ/2 and the allowed wavelengths are λ = 2L/n, where n is a positive integer. The simplest pattern, n = 1, has one antinode at the centre. A strong answer earns marks for these points. A node is a point of zero displacement at all times, produced where the two travelling waves are always in antiphase and cancel by superposition. An antinode is a point of maximum displacement, produced where the two travelling waves are always in phase and reinforce by superposition. The distance between adjacent nodes, or between adjacent antinodes, is λ/2, so the distance from a node to the next antinode is λ/4. For a string fixed at both ends, the fixed ends must be nodes, giving L = nλ/2 and allowed wavelengths λ = 2L/n for n = 1, 2, 3, ... A common slip: Treating a node as a point of minimum but non-zero displacement. Instead, stating that at a node the displacement is exactly zero at every instant. Exam tip: Sketch the string pattern and label nodes and antinodes before writing any explanation, so your description matches the diagram.
Key words
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Node
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Antinode
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Stationary wave
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Allowed wavelengths
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See every definition
- Node
- A point of permanently zero displacement, where the two waves always cancel because they arrive in antiphase.
- Antinode
- A point of maximum displacement, where the waves always reinforce because they arrive in phase.
- Stationary wave
- A pattern produced by superposition of two travelling waves that stores energy rather than transporting it along the string.
- Allowed wavelengths
- For a string of length L fixed at both ends, the ends must be nodes, so λ = 2L/n where n is a positive integer.
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