IBDP Physics SL Cheat sheet - C.5 Doppler effect | IBDP Physics Cheatsheets

Core idea

Doppler effect = apparent change in observed frequency (and therefore wavelength) due to relative motion between source and observer.
For an approaching source/observer: observed frequency increases and observed wavelength decreases.
For a receding source/observer: observed frequency decreases and observed wavelength increases.
The effect applies to sound waves and electromagnetic waves.
For sound, the wave travels through a medium, so it matters whether the source moves or the observer moves.
For light, use redshift and blueshift to describe the change in wavelength/frequency.

This diagram shows wavefronts bunched up in front of a moving source and spread out behind it. It is ideal for explaining why an observer ahead detects a higher frequency while an observer behind detects a lower frequency. Source

Wavefront interpretation

In wavefront diagrams, a moving source emits successive wavefronts from different positions.
Ahead of the source, wavefronts are closer together $arrow$ shorter wavelength $arrow$ higher frequency.
Behind the source, wavefronts are further apart $arrow$ longer wavelength $arrow$ lower frequency.
If the observer moves through the wave, they meet wavefronts more often when moving towards the source and less often when moving away.
In exams, identify clearly whether the diagram shows a moving source or a moving observer.
Do not confuse a change in frequency with a change in wave speed.

Sound: key ideas

For sound, the speed of sound in the medium stays approximately constant for a given medium.
A moving source changes the spacing of wavefronts in the medium.
A moving observer changes how often wavefronts are encountered.
Therefore, moving source and moving observer cases use different equations.
In this syllabus, problems do not include both source and observer moving at the same time.
Use the sign that gives higher $f'$ for approaching and lower $f'$ for receding.

This image clearly compares compressed wavefronts in front of the source with stretched wavefronts behind it. It is especially useful for explaining the sound-wave version of the Doppler effect with a moving source. Source

HL only: sound equations

Moving source: $f' = f\dfrac{v}{v \pm u_s}$
Here, $f'$ = observed frequency, $f$ = source frequency, $v$ = wave speed in the medium, $u_s$ = source speed.
Use $v - u_s$ when the source approaches the observer $arrow$ higher observed frequency.
Use $v + u_s$ when the source recedes from the observer $arrow$ lower observed frequency.
Moving observer: $f' = f\dfrac{v \pm u_o}{v}$
Here, $u_o$ = observer speed; use $v + u_o$ for approaching, $v - u_o$ for receding.
These equations are for sound/mechanical waves, not for the full relativistic treatment of light.
In exam questions, first decide who is moving, then choose the correct formula, then choose the correct sign.

Light: Doppler shift

For light at speeds much smaller than $c$ , the syllabus uses: $\dfrac{\Delta f}{f} = \dfrac{\Delta \lambda}{\lambda} \approx \dfrac{v}{c}$
$c$ = speed of light, $v$ = relative speed between source and observer.
Approaching light source $arrow$ blueshift: wavelength decreases, frequency increases.
Receding light source $arrow$ redshift: wavelength increases, frequency decreases.
This approximation is valid only when $v \ll c$ .
Spectral line shifts let us determine radial speed: motion towards/away from us.

This figure shows how light from a moving source shifts to shorter wavelengths when approaching and longer wavelengths when receding. It is directly relevant to IB questions on spectral lines, stars and galaxies. Source

Astronomy applications

Shifted spectral lines provide evidence for the motion of stars and galaxies.
If known spectral lines are shifted to longer wavelengths, the object is moving away from Earth.
If known spectral lines are shifted to shorter wavelengths, the object is moving towards Earth.
This motion measured from Doppler shift is the radial motion along the line of sight.
In data questions, compare the observed wavelength with the rest wavelength of a spectral line.

This spectrum diagram shows absorption lines shifted relative to their normal positions, linking Doppler shift directly to astronomical measurement. It is useful for explaining how astronomers infer stellar motion from spectral data. Source

Practical uses

Medical Doppler ultrasound measures blood flow speed using reflected ultrasound waves.
Radar speed guns use Doppler shift to measure the speed of vehicles.
In both cases, the wave returns from a moving object, so the frequency of the received wave is shifted.
Exam answers should link the application to frequency change caused by relative motion.

This diagram illustrates Doppler ultrasound measuring blood flow using reflected sound waves. It is a strong example of a real-world Doppler application commonly mentioned in IB Physics guidance. Source

Exam traps and quick rules

Approaching always means higher observed frequency.
Receding always means lower observed frequency.
For sound, the wave speed in the medium is not changed just because the source moves.
A moving source changes wavelength in the medium; a moving observer changes the rate of encountering wavefronts.
For light, know redshift, blueshift, and the approximation $\dfrac{\Delta f}{f} = \dfrac{\Delta \lambda}{\lambda} \approx \dfrac{v}{c}$ .
Do not use the sound equations for light unless the problem specifically supports an approximation.

Checklist: can you do this?

State what happens to observed frequency and wavelength when source and observer approach or recede.
Interpret a wavefront diagram for a moving source or moving observer.
Choose and use the correct HL sound equation and sign convention.
Explain redshift and blueshift using spectral lines.
Apply Doppler ideas to astronomy, radar, and medical ultrasound.

Written by:

Dr Shubhi Khandelwal

Qualified Dentist and Expert Science Educator

Shubhi is a seasoned educational specialist with a sharp focus on IB, A-level, GCSE, AP, and MCAT sciences. With 6+ years of expertise, she excels in advanced curriculum guidance and creating precise educational resources, ensuring expert instruction and deep student comprehension of complex science concepts.