Doppler Effect (DP IB Physics: SL): Exam Questions

The Doppler effect can be used to determine whether a star is moving away from or towards the Earth. 

Outline what is meant by 'Doppler effect' in this context.

In a laboratory, the spectrum of atomic hydrogen has a wavelength of 656.61 nm. The spectrum of a star observed on Earth is found to have the same line in the spectrum shifted to 656.68 nm.

(i) Calculate the speed of the star relative to the Earth.

[2]

(ii) Explain whether the star is moving towards or away from the Earth.

[2]

A second spectral line is observed at 567.34 nm in the laboratory. 

Determine the frequency of the spectral line from the star, as observed on Earth.

Explain the effect on the colour of light from the star if it were travelling towards the Earth.

An emission spectrum of light was obtained from a light source in a laboratory. 

The same wavelengths of light were observed on an emission spectrum from a distant galaxy, but were found to be redshifted.

Describe how you would expect the emission spectrum of the distant galaxy to look compared to the spectrum from the laboratory.

An astronomer observes that light from a galaxy has been shifted towards the blue end of an emission spectrum.

State and explain what can be deduced about the motion of the galaxy from this observation.

Hydrogen is an element of particular interest to cosmologists, as it can emit visible light waves.

A lot of useful information can be obtained by measuring the wavelength of the emitted light from the hydrogen in distant galaxies and comparing it to a laboratory sample.

Galaxies 1 and 2 are both moving relative to Earth. 

Compare the motions of galaxies 1 and 2 relative to Earth.

Calculate the speed of Galaxy 1 relative to Earth.

The diagram shows a stationary wave source, R, in water. The source produces waves with a constant frequency. The distance between each successive wavefront is equal to the wavelength of the waves produced by R.

The speed of the waves in water is v.

Sketch three successive wavefronts produced when the source is moving to the right at a speed of 0.75v. 

A scientist sits on a boat to the right of the source and measures the frequency of the waves as they approach.

Explain the observations the scientist will make.

Police use radar to detect speeding cars. A police officer stands at the side of the road and points a radar device at an approaching car. The device emits microwaves, which reflect off the car and return to the device. The radar device measures the change in frequency between the emitted and received microwaves.

The frequency change is given by

Where  is the transmitter frequency,  is the speed of the car, and  is the wave speed.

Explain the reason for the change in frequency between the emitted and received microwaves.

Explain the origin of the factor of 2 in the equation .

The following data are available:

• Transmitter frequency = 36.0 GHz

• Frequency change = 4.03 kHz

• Speed limit on the road = 30 miles per hour (mph)

• 1 mile = 1.6 km

Determine whether the car is breaking the speed limit.

Two stars, A and B, in a binary system move in an anti-clockwise direction. Both stars emit light with wavelength λ = 5.89 × 10⁻⁷ m. An observer on Earth records fluctuations in the wavelength of the light between 5.86 × 10⁻⁷ m and 5.92 × 10⁻⁷ m.

Assume the stars have circular orbits around their common centre of mass.

Draw a diagram which indicates the position of the stars relative to the Earth when:

(i) there is no redshift.

[1]

(ii) the wavelength is recorded as 5.86 × 10⁻⁷ m from both stars.

[2]

The radius of orbit of star B is 4.98 × 10¹¹ m. 

Calculate the time taken for one orbit of star A about the common centre of mass.

Two stars, A and B, in a binary system, move in a clockwise direction around a common centre of mass.

On the diagrams below, draw and label arrows to show the positions of stars A and B corresponding to their spectra as observed on Earth.

When measured in the laboratory, one of the spectral lines of hydrogen has a wavelength of 4.942 × 10⁻⁷ m. The same hydrogen line in the spectrum of one of the stars fluctuates from its laboratory wavelength by ± 0.310 × 10⁻⁷ m, and the line in the spectrum of the other star fluctuates by ± 0.994 × 10⁻⁷ m. Both stars have the same time period.

Calculate the orbital velocity of each star in the binary system and determine which of the stars, A or B, is faster.

In a different binary star system, also rotating clockwise, star C has an orbital velocity of 8.92 × 10⁷ m s⁻¹ and star D an orbital velocity of 1.20 × 10⁷ m s⁻¹. Both stars have the same orbital period.

On the diagram below, identify the positions of stars C and D and draw the absorption spectra as star C moves towards Earth and star D moves away from Earth.