Explain how stationary waves are formed in a stretched string fixed at both ends, and describe two ways in which a stationary wave differs from a progressive wave.

AQA A-Level Physics (7408) — 3.3.1 Progressive and Stationary Waves · Explain · 5 marks · View as Markdown

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

When a stretched string fixed at both ends is plucked, a stationary wave pattern can be formed.

Model answer (5 marks)

A wave is generated when the string is plucked and travels to the fixed ends. At each fixed end the wave is reflected with the same amplitude but inverted phase. The incident and reflected waves travel in opposite directions and superpose, producing a pattern of nodes and antinodes that does not move along the string – a stationary wave.

1. Energy transfer: a stationary wave does not transfer energy along the string, whereas a progressive wave carries energy from one point to another.
2. Amplitude variation: in a stationary wave different points have different amplitudes – nodes have zero amplitude and antinodes have maximum amplitude – whereas a progressive wave has the same amplitude at all points along the wave.
3. Phase relationship: in a stationary wave all points between two adjacent nodes oscillate in phase, while points on opposite sides of a node are in antiphase; in a progressive wave the phase changes continuously along the wave.

Examiner tips

  • Use the word ‘reflect’ and ‘superpose’ to show understanding of wave behaviour; mention nodes and antinodes; compare energy transfer and amplitude; keep answer concise and use correct terminology.
  • Structure answer: first explain formation (wave, reflection, superposition), then list two differences with clear contrast.
  • Use UK spelling (e.g., ‘behaviour’).

Common mistakes

  • Confusing stationary wave with progressive wave – forgetting that stationary waves have no net energy transfer; incorrectly stating that all points in a stationary wave have the same amplitude; mixing up nodes and antinodes or mislabeling phase relationships.

Mark scheme (5 marks)

  1. A wave travels along the string and reflects at the fixed end / boundary
  2. The incident wave and the reflected wave overlap / superpose / travel in opposite directions
  3. A stationary wave does not transfer energy (along the string / between the fixed ends), whereas a progressive wave does transfer energy
  4. In a stationary wave, different points vibrate with different amplitudes (some points do not vibrate at all — nodes — and some vibrate with maximum amplitude — antinodes), whereas in a progressive wave all points have the same amplitude
  5. In a stationary wave, all points between two adjacent nodes oscillate in phase with each other (points on opposite sides of a node are in antiphase), whereas in a progressive wave there is a continuous phase change along the wave

Key terms in this question

stationary wave · progressive wave

Related

More Progressive and Stationary Waves questions

▶ Try answering this question with AI marking (free) →