Explain why two stationary observers, one positioned directly in front of a train and one positioned directly behind the train, detect different frequencies from the train's whistle as the train moves towards the first observer at constant velocity.

IB DP Physics Higher Level (2023 syllabus) — C.5 Doppler effect · Explain · 4 marks · View as Markdown

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

A train moves at constant velocity along a straight track whilst sounding its whistle at a constant frequency. One observer stands on the track ahead of the train and a second observer stands on the track behind the train.

Model answer (4 marks)

The train emits sound waves that travel outward at the speed of sound in all directions from each successive position of the source.

In front of the train the wavefronts are compressed (wavelength is shorter) because the source moves towards the front observer between successive emissions.

Behind the train the wavefronts are stretched (wavelength is longer) because the source moves away from the rear observer between successive emissions.

Since frequency is inversely proportional to wavelength (for a fixed wave speed), the front observer detects a higher frequency than the emitted frequency and the rear observer detects a lower frequency, so the two observers detect different frequencies from each other.

Examiner tips

  • Use the word ‘compress’ for the front and ‘stretch’ for the rear to show understanding of wavefront motion. Show the relationship f = v/λ to link wavelength changes to frequency. Mention that the source speed is constant and the sound speed is constant.
  • common_mistakes
  • :
  • Confusing the direction of motion with the direction of wave propagation. Forgetting to state that the wavelength changes, not the source frequency. Using the wrong sign for the frequency shift (higher in front, lower behind).

Mark scheme (4 marks)

  1. The train emits sound waves that travel outward at the speed of sound in all directions from each successive position of the source.
  2. In front of the train the wavefronts are compressed (wavelength is shorter) because the source moves towards the front observer between successive emissions.
  3. Behind the train the wavefronts are stretched (wavelength is longer) because the source moves away from the rear observer between successive emissions.
  4. Since frequency is inversely proportional to wavelength (for a fixed wave speed), the front observer detects a higher frequency than the emitted frequency and the rear observer detects a lower frequency, so the two observers detect different frequencies from each other.

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