Explain how the principle of superposition accounts for the formation of a standing wave when a transverse wave on a stretched string reflects from a fixed end.

IB DP Physics Higher 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).

A transverse progressive wave travels along a stretched string and undergoes reflection at a fixed end, producing a standing wave pattern.

Model answer (4 marks)

A transverse wave travelling along a stretched string meets a fixed end and is reflected, producing an incident wave and a reflected wave that travel in opposite directions but have the same frequency, speed and wavelength.

The principle of superposition states that the resultant displacement at any point on the string is the algebraic sum of the displacements of the two waves at that point.

Where the incident and reflected waves are always 180° out of phase (antiphase) the displacements cancel at every instant, giving a node with zero displacement.

Where the waves are always 0° out of phase (in phase) their displacements add, giving a maximum amplitude – an antinode. The combination of nodes and antinodes forms a stationary pattern that does not travel along the string.

Examiner tips

  • State that the reflected wave has the same frequency and speed as the incident wave. Explain that superposition gives the resultant displacement. Identify nodes as points of complete cancellation and antinodes as points of maximum constructive interference. Mention that the pattern is stationary because the two waves travel in opposite directions.
  • common_mistakes
  • :
  • Failing to note that the reflected wave has the same frequency and speed. Confusing nodes with antinodes. Using vague terms like "overlap" instead of "superposition".

Mark scheme (4 marks)

  1. The incident wave and the reflected wave travel in opposite directions along the string with the same frequency (and speed/wavelength).
  2. The principle of superposition states that the resultant displacement at any point is the vector sum (algebraic sum) of the displacements of the two waves at that point.
  3. At certain points (nodes) the two waves are always in antiphase, so their displacements cancel at all times, giving zero resultant displacement.
  4. At antinodes the waves are always in phase, so their displacements reinforce to give maximum amplitude, resulting in a pattern that does not travel along the string.

Key terms in this question

principle of superposition · standing wave

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