OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
Stationary waves: (d) nodes and antinodes
A stationary wave forms when two identical progressive waves travelling in opposite directions superpose.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 5 of 8
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A stationary wave forms when two identical progressive waves travelling in opposite directions superpose. At a node the two displacements always cancel, so the resultant displacement stays zero and the point never moves. At an antinode the two displacements always reinforce, so the resultant displacement oscillates with maximum amplitude. Nodes and antinodes are fixed in space, spaced half a wavelength apart, and adjacent nodes and antinodes are separated by one quarter of a wavelength. Energy is not transferred past a node; it is stored between nodes. For a string fixed at both ends, the ends must be nodes, so the shortest pattern has one antinode at the centre.
What earns the marks
- A node is a point of permanently zero resultant displacement where two waves always cancel.
- An antinode is a point of maximum resultant displacement where two waves always reinforce.
- Nodes and antinodes are stationary in position, unlike the travelling wave crests.
- Adjacent nodes are separated by λ/2; a node and the next antinode are separated by λ/4.
- No net energy transfer occurs past a node in a stationary wave.
Common mistakes and how to put them right
Thinking nodes are points that move slowly.
Put it right: Nodes never move, because the two displacements cancel at every instant.
Confusing node spacing with wavelength.
Put it right: The node-to-node distance is λ/2, not λ.
Believing energy travels along the whole stationary wave.
Put it right: Energy is stored between nodes and is not transferred past a node.
Assuming an antinode is always a displacement maximum at every instant.
Put it right: The antinode oscillates between positive and negative maximum displacement.
Exam tips
- Sketch the envelope of the stationary wave and mark nodes where the envelope touches zero.
- Count node-to-node gaps and multiply by two to find the wavelength before substituting into v = fλ.
- Check whether the boundary is fixed (node) or free (antinode) before choosing the pattern.
- State clearly that nodes arise from cancellation and antinodes from reinforcement.
Try the lesson
The start of the Stationary waves: (d) nodes and antinodes lesson, made from checked teaching notes for this specification point.
Listen
A stationary wave forms when two identical progressive waves travelling in opposite directions superpose. At a node the two displacements always cancel, so the resultant displacement stays zero and the point never moves. At an antinode the two displacements always reinforce, so the resultant displacement oscillates with maximum amplitude. Nodes and antinodes are fixed in space, spaced half a wavelength apart, and adjacent nodes and antinodes are separated by one quarter of a wavelength. Energy is not transferred past a node; it is stored between nodes. For a string fixed at both ends, the ends must be nodes, so the shortest pattern has one antinode at the centre. A strong answer earns marks for these points. A node is a point of permanently zero resultant displacement where two waves always cancel. An antinode is a point of maximum resultant displacement where two waves always reinforce. Nodes and antinodes are stationary in position, unlike the travelling wave crests. Adjacent nodes are separated by λ/2; a node and the next antinode are separated by λ/4. Exam tip: Sketch the envelope of the stationary wave and mark nodes where the envelope touches zero.
Key words
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Node
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Antinode
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Node and antinode spacing in terms of wavelength
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Energy storage rather than transfer
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See every definition
- Node
- A point of permanently zero resultant displacement where two waves always cancel.
- Antinode
- A point of maximum resultant displacement where two waves always reinforce.
- Node and antinode spacing in terms of wavelength
- Adjacent nodes are separated by half a wavelength, and a node and the next antinode are separated by one quarter of a wavelength.
- Energy storage rather than transfer
- Energy is not transferred past a node; it is stored between nodes.
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