AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Stationary waves.
Full specification wording
Principle of superposition of waves and formation of stationary waves: Stationary waves.
A stationary wave forms when two progressive waves of the same frequency and similar amplitude travel in opposite directions through the same medium and superpose.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 1 of 7
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A stationary wave forms when two progressive waves of the same frequency and similar amplitude travel in opposite directions through the same medium and superpose. The superposition principle means displacements add algebraically at every point. In a string fixed at both ends, or a microwave reflection, the result has nodes where displacements always cancel and antinodes where they reinforce. Adjacent nodes are separated by half a wavelength, and the distance between a node and the next antinode is a quarter wavelength. Energy is not transferred along a stationary wave; energy is stored and exchanged between kinetic and potential forms. You should be able to describe experiments producing stationary waves and explain the formation in terms of superposition.
What earns the marks
- A stationary wave is formed by the superposition of two progressive waves of the same frequency travelling in opposite directions.
- At a node, the two waves always arrive in antiphase, so their displacements cancel and the resultant displacement is always zero.
- At an antinode, the two waves arrive in phase, so their displacements reinforce and the resultant displacement is maximum.
- The distance between adjacent nodes is half a wavelength, and the distance between a node and the next antinode is a quarter wavelength.
- Stationary waves do not transfer energy along the wave; energy is stored and exchanged between kinetic and potential energy.
- A stationary wave can be produced on a stretched string, in a microwave reflection experiment, or using a loudspeaker and reflecting surface.
Common mistakes and how to put them right
Confusing nodes with points of maximum displacement.
Put it right: Nodes have zero resultant displacement and antinodes have maximum resultant displacement.
Thinking that a stationary wave transfers energy from one end to the other.
Put it right: Energy is stored and exchanged, not propagated.
Assuming that any two waves superpose to give a stationary wave.
Put it right: The waves must have the same frequency and travel in opposite directions.
Exam tips
- Sketch the stationary wave pattern and label nodes and antinodes clearly before explaining the formation.
- Use the phrase ‘two progressive waves travelling in opposite directions’ when defining a stationary wave.
- When asked about distance, relate node spacing to half a wavelength and node-to-antinode spacing to a quarter wavelength.
Try the lesson
The start of the Principle of superposition of waves and formation of stationary waves: Stationary waves. lesson, made from checked teaching notes for this specification point.
Have a go first
Which statement describes a stationary wave formed on a stretched string?
Listen
A stationary wave forms when two progressive waves of the same frequency and similar amplitude travel in opposite directions through the same medium and superpose. The superposition principle means displacements add algebraically at every point. In a string fixed at both ends, or a microwave reflection, the result has nodes where displacements always cancel and antinodes where they reinforce. Adjacent nodes are separated by half a wavelength, and the distance between a node and the next antinode is a quarter wavelength. Energy is not transferred along a stationary wave; energy is stored and exchanged between kinetic and potential forms. You should be able to describe experiments producing stationary waves and explain the formation in terms of superposition. A strong answer earns marks for these points. A stationary wave is formed by the superposition of two progressive waves of the same frequency travelling in opposite directions. At a node, the two waves always arrive in antiphase, so their displacements cancel and the resultant displacement is always zero. At an antinode, the two waves arrive in phase, so their displacements reinforce and the resultant displacement is maximum. The distance between adjacent nodes is half a wavelength, and the distance between a node and the next antinode is a quarter wavelength. A common slip: Confusing nodes with points of maximum displacement. Instead, nodes have zero resultant displacement and antinodes have maximum resultant displacement. Exam tip: Sketch the stationary wave pattern and label nodes and antinodes clearly before explaining the formation.
Key words
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Principle of superposition
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Formation of stationary waves
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Nodes and antinodes
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Energy in stationary waves
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See every definition
- Principle of superposition
- Displacements add algebraically at every point.
- Formation of stationary waves
- Two progressive waves of the same frequency and similar amplitude travel in opposite directions through the same medium and superpose.
- Nodes and antinodes
- Nodes are where displacements always cancel and antinodes are where they reinforce.
- Energy in stationary waves
- Energy is not transferred along the wave but is stored and exchanged between kinetic and potential forms.
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