IB Physics HL C 5 Doppler Effect Questions

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

Exam points

Compare emitted and observed sound frequencies to infer whether a source is approaching or receding.
Read moving-source wavefront diagrams to explain how compressed spacing raises the observed frequency.
Use Δf/f ≈ 2v/c to infer vehicle speed from a reflected radar frequency shift.
Use red-shifted galaxy lines to infer recession speed and apply Hubble’s law to estimate distance.
Apply sound Doppler equations with the correct moving-source or moving-observer term and sign.

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: 4]

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 $340 \mathrm{~ms}^{-1}$ .

(a)

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 .

[ 4 ]

(i)

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

[ 2 ]

(ii)

Calculate v.

[ 2 ]

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

[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 2 — IB Physics HL — Option A

Figure for Question 2 — IB Physics HL — Option B

Figure for Question 2 — IB Physics HL — Option C

Figure for Question 2 — IB Physics HL — Option D

[Maximum number: 4]

Star A is a main sequence star.

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

(a)

The peak wavelength of the radiation from Star A is measured by an observer on Earth. The observed wavelength is 0.007 % less than the peak wavelength emitted by Star A (about 560 nm).

Outline how this difference arises.

[ 2 ]

(b)

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

[ 2 ]

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

Allow ECF for MP2.

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

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Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question 2

Question 3

Question (a)

Question (b)