C.5 Doppler effect

UNIT SYLLABUS

SL/HL 2 hours SL + 2 hours HL

The Doppler effect is the pitch-bend of physics: relative motion between a wave source and an observer changes the observed frequency. A source moving towards you crowds its wavefronts together (higher frequency); moving away, it stretches them out. For light, the same physics — in the approximation $v \ll c$ — becomes the astronomer's speedometer: redshifted spectral lines reveal receding galaxies, blueshift approaching ones, and tiny periodic shifts betray planets tugging their stars. HL adds the exact formulas for moving sources and moving observers of sound, which differ subtly and testably.

Guiding Questions

? Why does relative motion between source and observer change the observed frequency?
? How does the Doppler effect reveal the motion of astronomical objects?

✓ What the IB expects you to master

Describe the Doppler effect for sound and for electromagnetic waves.
Sketch and interpret wavefront diagrams for moving sources and moving observers.
Use the light approximation $\frac{\Delta f}{f} = \frac{\Delta\lambda}{\lambda} \approx \frac{v}{c}$ for $v \ll c$ .
Explain how spectral-line shifts reveal the motion of stars and galaxies (red/blue shift).
HL: apply the sound formulas — moving source $f' = f\left(\frac{v}{v \pm u_s}\right)$ and moving observer $f' = f\left(\frac{v \pm u_o}{v}\right)$ — choosing signs physically.

1 Key Formulas

Doppler (light, v ≪ c)

\frac{\Delta f}{f} = \frac{\Delta\lambda}{\lambda} \approx \frac{v}{c}

Moving source (HL)

f' = f\left(\frac{v}{v \pm u_{s}}\right)

Moving observer (HL)

f' = f\left(\frac{v \pm u_{o}}{v}\right)

2 Exam Preparation & Topic Explanations

Getting the signs right every time

Do not memorise sign rules — reason them. Approach must raise frequency, recession must lower it. Write the formula, then choose the sign in the denominator (source) or numerator (observer) that produces the physically required direction of change.

For light, use the approximation formula and always state $v \ll c$ ; the exact relativistic formula is not required.

Pro Exam Strategy

Moving source changes the wavelength in the medium; moving observer changes the rate of interception. Different physics, different formulas.
The frequency is constant while approaching (not rising!) — it jumps to a lower constant after passing.
Redshift = longer wavelength = recession. Blueshift = approach. Two words, two marks.
Rotating bodies (the Sun, galaxies) show line BROADENING — one edge approaches while the other recedes.

3 MCQ Practice

Q1. An ambulance siren sounds higher-pitched as it approaches because:

The siren frequency actually increases
The sound travels faster towards the observer
Successive wavefronts are emitted from positions closer to the observer, compressing the wavelength
The amplitude of the sound increases

Q2. A hydrogen line at 656.3 nm appears at 662.9 nm in a galaxy's spectrum. The galaxy is:

Approaching at about 1% of $c$
Receding at about 1% of $c$
Approaching at about 3% of $c$
Receding at about 3% of $c$

Q3. For sound, a source approaching a stationary observer at speed $u$ and an observer approaching a stationary source at the same speed give:

Exactly the same observed frequency
Slightly different frequencies, because the two situations are physically distinct
The same frequency only if $u > v$
Different frequencies for light but the same for sound

4 Short Answer Questions

PDF

Download the practice worksheet

All questions from this unit + answer key — free, printable.

↓

Formula Booklet →

Every data-booklet equation, searchable.

Simulations →

See this physics in motion.

Daily Question →

Practise one concept a day.

← Previous unit

C.4 Standing waves and resonance

Next unit →

D.1 Gravitational fields

Stuck on Doppler effect?

Get it explained properly — 1-on-1, by a specialist who has taught this unit for 13+ years. Newtonine students average 6.8 in IB Physics.

Book a Free Consultation