C.5 Doppler effect (AHL)

IB Physics HL· Theme C (Wave Behaviour) > C.5 Doppler effect (AHL)· 20 min read

1. 1. Physical Origin of the Doppler Effect★★☆☆☆⏱ 6 min

The Doppler effect describes the change in observed frequency of a wave when the source and observer move relative to one another. It occurs for all wave types, including sound, light, and water waves.

📘 Definition

Doppler Effect

The change in the frequency of a wave observed by a detector moving relative to the wave source, caused by relative motion along the line connecting source and observer.

The physical cause of the shift differs for moving sources versus moving observers:

A source moving towards an observer emits each new wavefront closer to the previous one, compressing wavelength in the direction of motion.
An observer moving towards a stationary source encounters more wavefronts per unit time, because their speed relative to wavefronts is higher.

📐 Worked Example

A sound source moves towards a stationary observer. Explain why observed frequency is higher than source frequency.

1
When the source moves towards the observer, each successive wavefront is emitted from a position closer to the observer than the previous wavefront.
2
This reduces the distance between adjacent wavefronts, so the wavelength in the direction of the observer is shorter than the source wavelength.
3
The speed of sound in air is constant for a fixed medium, so $v = f^{'} λ^{'}$ . A lower $λ^{'}$ gives a higher observed frequency $f^{'}$ .

Exam tip:

Motion towards always increases observed frequency; motion away always decreases it. Use this rule to check your calculations.

2. 2. Non-Relativistic Doppler Formulas★★★☆☆⏱ 8 min

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For relative speeds much less than the speed of light ( $v ≪ c$ ), which applies to almost all sound problems on IB exams, we use the standard non-relativistic Doppler formula:

f' = f \frac{v \pm v_o}{v \mp v_s}

📘 Definition

Non-relativistic Doppler Shift

f' = f \frac{v \pm v_o}{v \mp v_s}

Formula for observed frequency for non-relativistic motion relative to a medium. $v_{o}$ is observer speed, $v_{s}$ is source speed relative to the medium.

📐 Worked Example

A car horn emits 400 Hz and moves towards a stationary observer at 25 m/s. Speed of sound is 340 m/s. Calculate the observed frequency.

1
Identify values: $f = 400$ Hz, $v_{s} = 25$ m/s, $v_{o} = 0$ , $v = 340$ m/s. Source moves towards observer, so subtract $v_{s}$ from the denominator.
2
$f' = 400 \times \frac{340 + 0}{340 - 25}$
3
$f' = 400 \times \frac{340}{315} \approx 432 \text{ Hz}$
4
Check: source moves towards observer, so frequency should be higher than 400 Hz. This matches our result.

3. 3. Doppler Effect for Light★★★☆☆⏱ 6 min

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Light does not require a medium, so the Doppler shift for light depends only on the relative speed between source and observer. For IB HL, we only use the non-relativistic approximation for $v ≪ c$ , given by:

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

Where $Δ λ = λ^{'} - λ$ is the change in wavelength, $v$ is the relative speed along the line of sight, and $c$ is the speed of light. A receding source gives a positive $Δ λ$ (longer wavelength, called redshift), while an approaching source gives a negative $Δ λ$ (shorter wavelength, called blueshift).

📘 Definition

Redshift

Doppler shift of light from a receding source that increases observed wavelength, shifting it towards the red end of the visible spectrum.

📐 Worked Example

A hydrogen spectral line from a distant galaxy has a rest wavelength of 656 nm, and is measured at 682 nm on Earth. Calculate the recessional speed of the galaxy.

1
Calculate $Δ λ = 682 - 656 = 26$ nm, $λ = 656$ nm, $c = 3.0 \times 1 0^{8}$ m/s.
2
$v = c \frac{\Delta \lambda}{\lambda}$
3
$v = 3.0 \times 10^8 \times \frac{26}{656} \approx 1.2 \times 10^7 \text{ m/s}$
4
Check: wavelength increased, so the galaxy is moving away from Earth, which matches our positive speed result.

Exam tip:

Always confirm that a longer wavelength corresponds to a receding source, and shorter wavelength corresponds to an approaching source.

4. 4. Practical Applications and Reflected Waves★★★★☆⏱ 7 min

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Common practical applications of the Doppler effect tested in IB exams include:

Radar speed guns: measure vehicle speed via frequency shift of reflected radio waves
Ultrasound: measure blood flow via shift from reflected waves off moving blood cells
Astronomy: measure galaxy recessional speed to study cosmic expansion

For reflected waves off a moving object, you must calculate two sequential Doppler shifts: first the moving object acts as a moving observer, then as a moving source emitting the reflected wave.

📐 Worked Example

A 5.0 MHz ultrasound wave is reflected off blood moving towards the probe at 0.50 m/s. Speed of ultrasound in tissue is 1500 m/s. Calculate the frequency shift.

1
First step: blood acts as a moving observer towards the stationary source.
2
$f' = f \frac{v + v_{\text{blood}}}{v} = 5.0 \times 10^6 \times \frac{1500 + 0.5}{1500} = 5001667 \text{ Hz}$
3
Second step: blood acts as a moving source emitting frequency $f^{'}$ towards the stationary probe.
4
$f'' = f' \frac{v}{v - v_{\text{blood}}} = 5001667 \times \frac{1500}{1500 - 0.5} \approx 5003333 \text{ Hz}$
5
$\Delta f = f'' - f = 3300 \text{ Hz} = 3.3 \text{ kHz}$

5. Common Pitfalls

Wrong move:

Adding $v_{s}$ to the denominator when a source moves towards an observer

Why:

Sign convention is often misremembered, leading to the opposite frequency shift

Correct move:

Use the mnemonic: towards = subtract $v_{s}$ from the denominator, add $v_{o}$ to the numerator; away = reverse the signs

Wrong move:

Using separate source and observer speed formulas for light, with medium-dependent terms

Why:

Light does not travel through a medium, so the formula only depends on relative speed

Correct move:

Use $\frac{Δ λ}{λ} = \frac{v}{c}$ for light, where $v$ is the relative speed along the line of sight

Wrong move:

Claiming redshift means higher observed frequency

Why:

Redshift is defined as a shift to longer wavelength, which corresponds to lower frequency

Correct move:

Remember: redshift = longer wavelength, lower frequency; blueshift = shorter wavelength, higher frequency

Wrong move:

Calculating only one Doppler shift for a reflected wave off a moving object

Why:

Most problems only require one shift, so it is easy to miss the second shift for reflections

Correct move:

Always calculate two sequential shifts: one for the moving object as observer, one as moving source

Wrong move:

Calculating a Doppler shift for motion perpendicular to the line of sight

Why:

The Doppler effect only arises from motion along the line connecting source and observer

Correct move:

If there is no component of velocity along the line of sight, the Doppler shift is zero

6. Quick Reference Cheatsheet

Scenario	Formula	Rule of Thumb
Moving observer, stationary source	$f^{'} = f \frac{v \pm v _{o}}{v}$	Towards: +, Away: -
Moving source, stationary observer	$f^{'} = f \frac{v}{v \mp v _{s}}$	Towards: -, Away: +
Non-relativistic light	$\frac{Δ λ}{λ} = \frac{v}{c}$	Receding: +v = redshift
Reflected wave off moving object	Two sequential shifts	First observer, then source

7. Frequently Asked

Do I need the relativistic Doppler formula for IB HL?

No. IB Physics AHL only requires the non-relativistic approximation for speeds $v ≪ c$ , which covers all exam questions.

Why are the formulas different for moving sources vs moving observers?

The shift arises from different physical causes: wavelength compression for moving sources, and altered relative wave speed for moving observers.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · 2
Doppler shift for moving sound source
2022 · 1
Galaxy redshift calculation
2021 · 2
Ultrasound reflected frequency shift

What's Next

Mastery of the Doppler effect is critical for IB Physics HL exams, as it regularly appears in both Paper 1 calculation and Paper 2 extended response questions. This core wave phenomenon connects fundamental wave properties to real-world applications in medicine, engineering and astronomy, and builds on your understanding of basic wave behaviour. The concepts you learn here provide a foundation for astrophysics topics like cosmic expansion, and for relativity, where relativistic Doppler shifts are introduced for high-speed motion. Practising sign convention and reflected wave problems will ensure you earn full marks on this common exam topic.