Explain how the amplitude of a standing wave varies along its length, and distinguish between a node and an antinode in terms of the energy of the standing wave.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A standing wave is established on a string stretched between two fixed supports.
Model answer (4 marks)
The amplitude of a standing wave is not uniform along the string; it varies from zero at the nodes to a maximum at the antinodes.
A node is a point where the displacement of the string is always zero – the two travelling waves cancel each other by destructive interference at that point.
An antinode is a point where the displacement is always maximum – the two travelling waves add constructively at that point.
Because the amplitude is zero at nodes, the kinetic and potential energies there are zero; at antinodes the amplitude is greatest, so the kinetic and potential energies are maximum. Thus energy is not uniformly distributed along a standing wave, unlike a progressive wave.
A node is a point where the displacement of the string is always zero – the two travelling waves cancel each other by destructive interference at that point.
An antinode is a point where the displacement is always maximum – the two travelling waves add constructively at that point.
Because the amplitude is zero at nodes, the kinetic and potential energies there are zero; at antinodes the amplitude is greatest, so the kinetic and potential energies are maximum. Thus energy is not uniformly distributed along a standing wave, unlike a progressive wave.
Examiner tips
- Use the terms ‘node’ and ‘antinode’ explicitly; explain the interference that creates them.
- Show the relationship between amplitude and energy (kinetic + potential).
- Mention that nodes have zero energy while antinodes have maximum energy.
Common mistakes
- Confusing nodes with antinodes or vice versa.
- Saying the energy is the same at all points; ignoring the zero energy at nodes.
- Using ‘maximum’ for nodes or ‘zero’ for antinodes incorrectly.
Mark scheme (4 marks)
- The amplitude of a standing wave is not uniform along its length but varies from zero at nodes to a maximum at antinodes.
- A node is a point of zero displacement / zero amplitude where destructive superposition of the two travelling waves is permanent.
- An antinode is a point of maximum displacement / maximum amplitude where constructive superposition of the two travelling waves is permanent.
- Nodes carry no energy / have zero kinetic and potential energy, whereas antinodes carry maximum energy, so energy is not uniformly distributed along a standing wave (unlike a progressive wave).
Key terms in this question
standing wave · node · antinode · amplitude
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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