IB Physics HL C.5 Doppler effect questions

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Question 1

Multiple choiceEasy1 mark

A source emits light with wavelength 600 nm and moves directly away from an observer at 1.5×106 m s−11.5 \times 10^6\ \text{m s}^{-1} Take the speed of light as 3.0×108 m s−13.0 \times 10^8\ \text{m s}^{-1} What is the magnitude of the relative change in wavelength, expressed as a percentage?

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Answer: C. For light, the magnitude of the relative wavelength change is approximately v/cv/c Thus v/c=(1.5×106)/(3.0×108)=5.0×10−3=0.50%v/c=(1.5 \times 10^6)/(3.0 \times 10^8)=5.0 \times 10^{-3}=0.50\%

A: converts the fractional change to a percentage using a factor of 10 rather than 100.
B: introduces an erroneous factor of 1/21/2
D: shifts the decimal point one place too far when converting the fraction to a percentage.

Remember: multiply a fractional change by 100 to express it as a percentage.

Question 2

Paper 2Hard10 marks

A sound emitter moves uniformly through still air. At one instant, the distance between adjacent wavefronts is 0.646 m ahead of the emitter and 0.714 m behind it. The speed of sound in the air is 340 m s⁻¹. In a second arrangement, the emitter is stationary and a detector moves towards it at the speed found in (a). The emitter has the same frequency in both arrangements.

(a)

Determine the emitted frequency and the speed of the emitter. Show your reasoning.

[4]
(b)

Sketch wavefront diagrams for (i) the sound emitter moving towards a stationary detector and (ii) a stationary emitter with the detector moving towards it. Indicate the directions of motion and the relative spacing of the wavefronts.

[2]
(c)

Calculate the frequency detected in each sound arrangement. Give your answers to three significant figures.

[2]
(d)

A light beacon moves towards an observer. State how the detected frequency and wavelength compare with those emitted, and state one relevant difference between light waves and sound waves.

[2]

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