Explain how the superposition of two waves produces a standing wave, and state the conditions on the two waves that are necessary for this to occur.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Two waves travel in opposite directions along a stretched string. At certain frequencies, a stable pattern is observed in which some points on the string remain stationary while others vibrate with maximum amplitude.
Model answer (4 marks)
Two waves travelling along the string overlap; at each point the displacement is the vector sum of the two individual displacements (superposition). For a standing wave the two waves must:
1. Have the same frequency (hence the same wavelength) and the same amplitude.
2. Travel in opposite directions.
Because they are opposite, at points where the waves are 180° out of phase (nodes) they cancel and the displacement is always zero. At points where they are in phase (antinodes) they add and give maximum amplitude.
1. Have the same frequency (hence the same wavelength) and the same amplitude.
2. Travel in opposite directions.
Because they are opposite, at points where the waves are 180° out of phase (nodes) they cancel and the displacement is always zero. At points where they are in phase (antinodes) they add and give maximum amplitude.
Examiner tips
- Show the superposition principle first, then list the two conditions (same f, opposite direction).
- Explain nodes/antinodes as phase relationships to justify the pattern.
Mark scheme (4 marks)
- The two waves overlap/superpose and the resultant displacement at each point is the vector sum of the individual displacements.
- The two waves must have the same frequency (and wavelength) and the same (or very similar) amplitude.
- The two waves must travel in opposite directions.
- At nodes the two waves are always in antiphase (phase difference of π / 180°), so they destructively interfere and the displacement is permanently zero; at antinodes they are always in phase, giving maximum constructive interference and maximum amplitude.
Key terms in this question
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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