IB Physics HL C.5 Doppler effect Questions

SLSL HLHL

Practise C.5 by comparing source and observer frequencies, applying sound Doppler equations, and using spectral shifts to infer astronomical motion.

90 questions in this syllabus scope, with question parts counted together.

Exam points & syllabus

Exam points

Describe Doppler shift as a change in detected frequency caused by source–observer motion along the line of sight.
Approach increases detected frequency and recession decreases it; use the actual radial velocity rather than total motion alone.
A moving source compresses wavefront spacing ahead and stretches it behind while wave speed remains fixed in a stationary medium.
A moving observer changes its wavefront encounter rate without changing the wavelength emitted by a stationary source.
Draw successive circular wavefronts from the source’s earlier positions, with closer spacing ahead of subsonic motion.
When a source passes an observer, interpret the frequency trace using approach before passage and recession afterwards, including changing speed.
Treat received intensity and frequency separately: changing distance affects intensity, while radial motion produces Doppler shift.
For low-speed light, use the magnitudes |Δf|/f ≈ |Δλ|/λ ≈ v/c; signed frequency and wavelength shifts have opposite signs.
Use the emitted or laboratory value as the reference when calculating a fractional spectral shift, and keep units consistent.
State the low-speed assumption when using the approximate light-shift relation; do not claim relativistic precision from an approximate result.
Compare the same spectral feature with its laboratory wavelength: red-shift means longer received wavelength and blue-shift means shorter.
Infer radial recession from a red-shift and approach from a blue-shift in a Doppler interpretation; name the motion explicitly when required.
Explain a blue-shift through approach and closer wavefront spacing; the wavefront mark can depend on the correct direction.
Measure the line shift relative to its rest value and apply the current Doppler relation to find a radial speed.
Systematic distant-galaxy red-shifts indicate recession and increasing separations, providing kinematic evidence against a static universe.
For multiple lines from one source, preserve a common fractional shift; a longer-wavelength line has a larger absolute wavelength change.
For binary spectra, trace each star’s velocity after the stated orbital rotation before choosing the direction of its shifted line.
For mechanical waves, distinguish source motion in the denominator from observer motion in the numerator.
With a stationary observer, use f′ = fc/(c − uₛ) for an approaching source and f′ = fc/(c + uₛ) for a receding source.
For a stationary source, use f′ = f(c + uₒ)/c for an approaching observer and f′ = f(c − uₒ)/c for recession.
Rearrange the selected Doppler equation to recover an unknown emitted frequency or speed, and interpret the speed’s sign physically.
For a moving source and stationary observer, calculate detected wavelength from λ′ = c/f′ using the detected frequency.
For reflected sound, apply two separate Doppler steps, identifying the moving source or observer on each leg.
After calculating the returned frequency, subtract the emitted value when the question asks for the frequency change.
Use the largest speed from the motion graph or the supplied prior result to obtain the greatest reflected shift.
For an observer between two stationary sources, assign opposite approach and recession signs and equate the two detected frequencies.
For wavefront encounters, calculate λ = c/f and combine the relative encounter speed with wave speed to obtain the observer’s speed and direction.
For a rotating source, use the maximum radial shift to obtain linear speed, then use ω = v/r with the orbital radius.

Covered syllabus points

C.5.1—Doppler effect C.5.2—Doppler wavefront diagrams C.5.3—Light Doppler approximation C.5.4—Spectral line shifts C.5.5 (HL)—Mechanical-wave Doppler formulas

[Maximum number: 2]

Two loudspeakers, A and B, are driven in phase and with the same amplitude at a frequency of 850 Hz . Point P is located 22.5 m from A and 24.3 m from B. The speed of sound is $340 \mathrm{~ms}^{-1}$ .

In another experiment, loudspeaker A is stationary and emits sound with a frequency of 850 Hz . The microphone is moving directly away from the loudspeaker with a constant speed v. The frequency of sound recorded by the microphone is 845 Hz .

Explain why the frequency recorded by the microphone is lower than the frequency emitted by the loudspeaker.

[Maximum number: 1]

A point source of sound is moving to the right at constant speed. The source emits sound waves of constant frequency. The speed of the source is less than the speed of sound. Which diagram correctly shows the wavefronts of the sound?

Figure for Question 1 — IB Physics HL — Option A

Figure for Question 1 — IB Physics HL — Option B

Figure for Question 1 — IB Physics HL — Option C

Figure for Question 1 — IB Physics HL — Option D

[Maximum number: 2]

Star A is a main sequence star.

The data for Star A and the Sun are given in a table.

Determine the speed, in $\mathrm{km} \mathrm{s}^{-1}$ , of Star A relative to Earth.

$\begin{aligned} v=\frac{\Delta \lambda}{\lambda} c=\frac{0.007}{100} \times 3 \times 10^{8}=21000 21 \mathrm{~km} \mathrm{~s}^{-1} \end{aligned}$

Allow ECF for MP2.

Do not award MP1 for use of the Doppler formulas for sound and mechanical waves.

[Maximum number: 2]

A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.

The wavelength of the light in the beam when emitted by the galaxy was 621.4 nm .

Explain, without further calculation, what can be deduced about the relative motion of the galaxy and the Earth.

[Maximum number: 2]

Calculate v.

$\begin{aligned} 845=850 \times \frac{340-v}{340} v=2.00<\mathrm{m} \mathrm{~s}^{-1}>- \end{aligned}$

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