Doppler Effect

Introduction

The Doppler effect is the observed change in frequency or wavelength caused by relative motion between source and observer. The guide treats both sound/mechanical waves and light, with astronomy, medicine, and radar as important applications.

Guide Focus

• Explain Doppler shifts using wavefront diagrams.
• Use approximate fractional shift for light when relative speeds are much less than c.
• Apply HL equations for moving sound sources or moving observers.

Key Concepts

1. Qualitative Doppler effect

When source and observer move closer together, wavefronts are received more frequently and the observed frequency increases. When they move apart, observed frequency decreases.

2. Light and spectral shifts

For light at speeds much smaller than c, delta f / f = delta lambda / lambda approximately equals v / c in magnitude. Redshift and blueshift of spectral lines reveal motion of stars and galaxies.

3. HL sound equations

For a moving source, f’ = f v / (v +/- us). For a moving observer, f’ = f (v +/- uo) / v. The sign is chosen by deciding whether motion makes wavefronts arrive more often or less often.

4. Applications

Medical ultrasound, radar speed measurement, and astronomical spectroscopy all use Doppler shifts to infer motion.

Common Mistakes

• Using the sound-wave formula for light.
• Choosing signs mechanically instead of checking whether frequency should increase or decrease.
• Including cases where both source and observer move, which the guide excludes.

Exam Tips

• First decide: should f’ be bigger or smaller than f?
• For light redshift, wavelength increases when the source is receding.
• Keep wave speed v for sound separate from source/observer speeds us and uo.

Practice Questions

Question 1 (Multiple Choice)

A sound source moves toward a stationary observer. What happens to the observed frequency?

A. It increases. B. It decreases. C. It stays the same. D. It becomes zero.

Question 2 (Structured Paper 2 Style)

A stationary observer hears a 500 Hz source moving toward them at 20 m s-1. The speed of sound is 340 m s-1.

(a) Calculate the observed frequency. [2 marks]

(b) State why the value is greater than 500 Hz. [1 mark]