Explain how the principle of superposition accounts for the formation of a standing wave when two identical waves travel in opposite directions along the same medium.

IB DP Physics Standard Level (2023 syllabus) — C.2 Wave model · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Two identical travelling waves of the same frequency, amplitude, and wavelength move in opposite directions along a stretched string.

Model answer (4 marks)

The principle of superposition states that when two waves meet, the resultant displacement at any point is the algebraic sum of the individual displacements.

When two identical waves travel in opposite directions, at some points the displacements are always opposite in sign (antiphase). These points are nodes, where the algebraic sum is zero at all times.

At other points the displacements are always in the same direction (in phase). These are antinodes, where the algebraic sum is twice the amplitude of one wave, giving the maximum displacement.

Because the nodes and antinodes are fixed in space, the pattern of constructive and destructive interference does not move along the string. Energy is stored in the oscillating pattern rather than transported, so the superposition of the two oppositely travelling waves produces a standing wave.

Examiner tips

  • Use the word ‘principle of superposition’ first. Show the node/antinodes idea with a brief description of phase. Mention that the pattern is stationary and energy is stored. Keep the answer to 4 concise sentences.

Common mistakes

  • Confusing travelling wave with standing wave. Forgetting to state that nodes have zero displacement. Using vague terms like ‘interference’ without linking to superposition.

Mark scheme (4 marks)

  1. The principle of superposition states that when two waves meet, the resultant displacement at any point is the vector (algebraic) sum of the individual displacements.
  2. At certain points (nodes), the two waves are always in antiphase, so their displacements cancel to give zero resultant displacement at all times.
  3. At antinodes, the two waves are always in phase, so their displacements add constructively, producing maximum amplitude (equal to twice the amplitude of each wave).
  4. The pattern of nodes and antinodes does not travel along the medium — energy is stored in the pattern rather than transported, which is why the superposition of the two oppositely travelling waves produces a standing (stationary) wave.

Key terms in this question

principle of superposition · standing wave

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