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AS · Practice questions · The Doppler effect

The shifting pitch.

Six original Cambridge-style questions on the Doppler formula, the direction of the shift, and redshift.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Mind the sign.

01
Analysis
[2 marks]

State what is meant by the Doppler effect.

  • It is the change in the observed frequency of a wave ✓
  • caused by relative motion between the source and the observer ✓
02
Analysis
[3 marks]

A train horn emits 500 Hz and approaches a stationary observer at 25 m s⁻¹. Taking the speed of sound as 340 m s⁻¹, find the observed frequency.

  • fₒ = fₛ v / (v − vₛ) = 500 × 340 / (340 − 25) ✓
  • = 500 × 340 / 315 ✓
  • fₒ = 540 Hz ✓
03
Analysis
[3 marks]

The same horn (500 Hz) now recedes from the observer at 25 m s⁻¹. Find the observed frequency.

  • fₒ = fₛ v / (v + vₛ) = 500 × 340 / 365 ✓
  • fₒ = 466 Hz ✓
04
Analysis
[2 marks]

Explain why the pitch of a siren appears to drop suddenly as it passes you.

  • While approaching, the wavefronts bunch up, so the observed frequency is higher than emitted ✓
  • As it passes and recedes, the wavefronts spread out, so the observed frequency drops below the emitted value ✓
05
Analysis
[2 marks]

Light from a distant galaxy is found to be redshifted. State what this tells us about the galaxy.

  • The wavelength is increased (frequency lowered), a Doppler shift for a receding source ✓
  • So the galaxy is moving away from us, evidence for an expanding Universe ✓
06
Analysis
[3 marks]

A car sounding its 300 Hz horn approaches at 40 m s⁻¹ (speed of sound 340 m s⁻¹). Find the observed frequency.

  • fₒ = 300 × 340 / (340 − 40) = 300 × 340 / 300 ✓
  • fₒ = 340 Hz ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.