Doppler effect, redshift and the expanding universeEdexcel A-Level Physics: Subtopic test

1. 1
   An ambulance travels along a straight road at a steady speed while its siren emits a constant note of frequency 700 Hz, measured by the driver. A pedestrian stands at the side of the road, and the ambulance drives past her.

   (a)

   The pedestrian hears the note from the siren as the ambulance approaches her. Which statement describes what she hears?

   [1 mark]

   • AThe frequency is lower than 700 Hz
   • BThe frequency is exactly 700 Hz
   • CThe frequency is higher than 700 Hz
   • DThe frequency rises and falls repeatedly

   (b)

   The driver also listens to the siren. What frequency does the driver hear?

   [1 mark]

   • A700 Hz, because there is no relative motion between the siren and the driver
   • BHigher than 700 Hz, because the ambulance is moving
   • CLower than 700 Hz, because the pedestrian is stationary
   • DHigher than 700 Hz, because the driver is moving towards the pedestrian

   (c)

   Explain why the pedestrian hears a higher frequency than 700 Hz as the ambulance approaches.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Astronomers study the light from a distant galaxy. The hydrogen line that has a wavelength of 656.3 nm when measured in a laboratory is observed in the galaxy's spectrum at a wavelength of 662.9 nm. Take $c = 3.00 \times 10^{8}$ m s⁻¹.

   (a)

   What is the redshift z of this galaxy?

   [1 mark]

   • A1.01
   • B0.0101
   • C0.0099
   • D0.101

   (b)

   Which conclusion about the galaxy is justified by the observation?

   [1 mark]

   • AIt is moving away from the Earth
   • BIt is moving towards the Earth
   • CIt is stationary relative to the Earth
   • DIt is hotter than the Sun

   (c)

   Calculate the speed at which the galaxy is receding from the Earth.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A galaxy is a distance of $4.5 \times 10^{24}$ m from Earth. Take the Hubble constant as $H_0 = 2.2 \times 10^{-18}$ s⁻¹ and $c = 3.00 \times 10^{8}$ m s⁻¹. A hydrogen line that has a wavelength of 486.1 nm in the laboratory is observed in light from this galaxy.

   (a)

   Calculate the speed at which this galaxy is receding from the Earth.

   [3 marks]

   (b)

   Calculate the wavelength at which the hydrogen line is observed from this galaxy.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Cosmologists use measurements of galaxy speeds and distances to estimate the age of the universe and to predict how it will end. Take $H_0 = 2.2 \times 10^{-18}$ s⁻¹ and 1 year = $3.16 \times 10^{7}$ s. Different research groups have measured values of the Hubble constant that disagree by about 8%, and observations of how galaxies rotate suggest that there is far more mass in galaxies than can be seen.

   (a)

   Estimate the age of the universe in years from the Hubble constant, and state two assumptions that you have made.

   [6 marks]

   (b)

   Discuss why the age and the fate of the universe are still controversial, referring to the Hubble constant and dark matter.

   [6 marks]

   Total for question 4: 12 marks

End of questions