AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
A graphical explanation of formation of stationary waves will be expected.
Full specification wording
Principle of superposition of waves and formation of stationary waves: A graphical explanation of formation of stationary waves will be expected.
Stationary waves form when two progressive waves of the same frequency and similar amplitude travel in opposite directions through the same medium.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 4 of 7
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Stationary waves form when two progressive waves of the same frequency and similar amplitude travel in opposite directions through the same medium. The principle of superposition means displacements add at every point. A graphical explanation shows two travelling waves, often one incident and one reflected, drawn at successive instants; adding their displacements point by point produces a pattern that no longer travels. At nodes, displacements always cancel because the waves are in antiphase; at antinodes, they reinforce in phase. The distance between adjacent nodes is half a wavelength.
For example: A string fixed at one end reflects a wave so incident and reflected waves interfere, giving nodes at fixed points and antinodes between them.
What earns the marks
- State that two progressive waves of the same frequency travel in opposite directions through the same medium.
- Apply the principle of superposition by adding displacements of the two waves at each point.
- Identify nodes as points of zero resultant displacement where the waves are in antiphase.
- Identify antinodes as points of maximum resultant displacement where the waves are in phase.
- Use a graph or diagram to show incident and reflected waves and their resultant at a chosen instant.
- Relate the node spacing to half a wavelength and note that the stationary wave pattern does not transfer energy.
Common mistakes and how to put them right
Treating a stationary wave as a single travelling wave.
Put it right by showing two opposite-travelling waves and their superposition.
Confusing nodes with points of maximum displacement.
Put it right by defining nodes as zero-displacement points and antinodes as maximum-displacement points.
Assuming all points on a stationary wave oscillate in phase.
Put it right by noting that points between adjacent nodes are in phase, but adjacent loops are in antiphase.
Exam tips
- Draw two separate travelling waves with the same wavelength and amplitude, then add their displacements at several points to show the resultant.
- Label nodes and antinodes clearly and mark one wavelength and the node spacing on the diagram.
- Use the phrase 'superposition of two waves travelling in opposite directions' when explaining formation.
Try the lesson
The start of the Principle of superposition of waves and formation of stationary waves: A graphical explanation of formation of stationary waves will be expected. lesson, made from checked teaching notes for this specification point.
Have a go first
Two identical progressive waves of amplitude A travel in opposite directions along a string. At a specific instant, the displacement-position graphs of the two waves perfectly overlap. What is the resultant displacement profile of the string at this instant?
Listen
Stationary waves form when two progressive waves of the same frequency and similar amplitude travel in opposite directions through the same medium. The principle of superposition means displacements add at every point. A graphical explanation shows two travelling waves, often one incident and one reflected, drawn at successive instants; adding their displacements point by point produces a pattern that no longer travels. At nodes, displacements always cancel because the waves are in antiphase; at antinodes, they reinforce in phase. The distance between adjacent nodes is half a wavelength. For example, a string fixed at one end reflects a wave so incident and reflected waves interfere, giving nodes at fixed points and antinodes between them. A strong answer earns marks for these points. State that two progressive waves of the same frequency travel in opposite directions through the same medium. Apply the principle of superposition by adding displacements of the two waves at each point. Identify nodes as points of zero resultant displacement where the waves are in antiphase. Identify antinodes as points of maximum resultant displacement where the waves are in phase. A common slip: Treating a stationary wave as a single travelling wave. Instead, showing two opposite-travelling waves and their superposition. Exam tip: Draw two separate travelling waves with the same wavelength and amplitude, then add their displacements at several points to show the resultant.
Key words
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Superposition of waves
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Opposite-travelling progressive waves
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Nodes and antinodes
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Energy in stationary waves
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See every definition
- Superposition of waves
- Displacements of two waves add at every point.
- Opposite-travelling progressive waves
- Two progressive waves of the same frequency and similar amplitude travel in opposite directions through the same medium.
- Nodes and antinodes
- At nodes displacements always cancel because the waves are in antiphase; at antinodes they reinforce in phase.
- Energy in stationary waves
- The stationary wave pattern does not transfer energy.
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