OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
Stationary waves: (a) stationary
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 OCR H556 specification (opens in a new tab) on .
- Point 1 of 8
- 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. Energy is not transferred along the wave; instead it is stored, oscillating between kinetic and potential forms. The pattern has fixed nodes, where displacement is always zero, and antinodes, where displacement varies with maximum amplitude. Adjacent nodes are separated by half a wavelength, λ/2, and the node-to-antinode distance is λ/4.
For example: A stretched string fixed at both ends reflects waves so that the reflected and incident waves superpose, producing a stationary wave whose allowed frequencies depend on the string length and tension.
What earns the marks
- A stationary wave is produced by the superposition of two progressive waves of the same frequency travelling in opposite directions.
- Nodes are points of permanently zero displacement; antinodes are points of maximum displacement amplitude.
- The separation between adjacent nodes is λ/2 and between a node and the nearest antinode is λ/4.
- No net energy is transferred along a stationary wave; energy oscillates between kinetic and potential stores.
- The boundary conditions of the medium, such as fixed ends of a string, determine which stationary wave patterns can form.
Common mistakes and how to put them right
Thinking a stationary wave travels along the medium.
Put it right by stressing that the pattern stays in fixed positions while individual particles oscillate.
Confusing nodes with points of maximum amplitude.
Put it right by defining a node as permanently zero displacement and an antinode as maximum amplitude.
Believing energy is transported along a stationary wave.
Put it right by explaining that energy is stored and exchanged between kinetic and potential forms within the pattern.
Exam tips
- Sketch the envelope of the stationary wave and label nodes and antinodes before answering.
- Use the relationships node-to-node = λ/2 and node-to-antinode = λ/4 to check numerical options.
- Eliminate options that claim energy is transferred along the wave or that the pattern moves.
Try the lesson
The start of the Stationary waves: (a) stationary lesson, made from checked teaching notes for this specification point.
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. Energy is not transferred along the wave; instead it is stored, oscillating between kinetic and potential forms. The pattern has fixed nodes, where displacement is always zero, and antinodes, where displacement varies with maximum amplitude. Adjacent nodes are separated by half a wavelength, λ/2, and the node-to-antinode distance is λ/4. For example, a stretched string fixed at both ends reflects waves so that the reflected and incident waves superpose, producing a stationary wave whose allowed frequencies depend on the string length and tension. A strong answer earns marks for these points. A stationary wave is produced by the superposition of two progressive waves of the same frequency travelling in opposite directions. Nodes are points of permanently zero displacement; antinodes are points of maximum displacement amplitude. The separation between adjacent nodes is λ/2 and between a node and the nearest antinode is λ/4. No net energy is transferred along a stationary wave; energy oscillates between kinetic and potential stores. A common slip: Thinking a stationary wave travels along the medium. Instead, stressing that the pattern stays in fixed positions while individual particles oscillate. Exam tip: Sketch the envelope of the stationary wave and label nodes and antinodes before answering.
Key words
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Superposition of oppositely travelling waves
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Nodes and antinodes
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Energy storage rather than transfer
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Boundary conditions and allowed patterns
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See every definition
- Superposition of oppositely travelling 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.
- Nodes and antinodes
- Nodes are points of permanently zero displacement, while antinodes are points where displacement varies with maximum amplitude.
- Energy storage rather than transfer
- No net energy is transferred along a stationary wave; instead energy is stored, oscillating between kinetic and potential forms.
- Boundary conditions and allowed patterns
- The boundary conditions of the medium, such as fixed ends of a string, determine which stationary wave patterns can form.
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