Doppler effect, redshift and the Hubble constantEdexcel International A Level Physics: Subtopic test

1. 1
   An ambulance sounds a siren of constant frequency 700 Hz as it drives at constant speed along a straight road towards a stationary observer standing by the roadside, passes her, and then drives away.

   (a)

   What does the observer hear while the ambulance is approaching her?

   [1 mark]

   • AA lower frequency and a longer wavelength than the siren emits
   • BThe same frequency as the siren emits, but louder
   • CA higher frequency and a longer wavelength than the siren emits
   • DA higher frequency and a shorter wavelength than the siren emits

   (b)

   What does the observer hear after the ambulance has passed her and is driving away at constant speed?

   [1 mark]

   • AA frequency higher than 700 Hz
   • BA constant frequency lower than 700 Hz
   • CExactly 700 Hz
   • DA frequency that decreases steadily

   (c)

   Explain why the observer hears a higher frequency than 700 Hz while the ambulance is approaching her.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A spectral line of hydrogen has a wavelength of 656 nm when measured in a laboratory. In the light from a distant galaxy the same line is measured at a wavelength of 662 nm. Use a speed of light of 3.00 × 10⁸ m s⁻¹ and a Hubble constant H₀ of 2.3 × 10⁻¹⁸ s⁻¹.

   (a)

   What can be deduced about the galaxy?

   [1 mark]

   • AIt is moving towards us, and the line is blueshifted
   • BIt is moving away from us, and the line is blueshifted
   • CIt is moving away from us, and the line is redshifted
   • DIt is stationary relative to us, and the line is redshifted

   (b)

   What is the recession speed of the galaxy?

   [1 mark]

   • A2.7 × 10⁶ m s⁻¹
   • B9.1 × 10⁻³ m s⁻¹
   • C2.7 × 10³ m s⁻¹
   • D2.7 × 10⁸ m s⁻¹

   (c)

   Calculate the distance to the galaxy in metres.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two research teams use different methods to measure the Hubble constant H₀. They obtain values of 2.2 × 10⁻¹⁸ s⁻¹ and 2.4 × 10⁻¹⁸ s⁻¹. One year is 3.16 × 10⁷ s. The age of the universe can be estimated using the Hubble constant.

   (a)

   Explain why 1/H₀ gives an estimate of the age of the universe, and calculate this age in years for H₀ = 2.2 × 10⁻¹⁸ s⁻¹.

   [3 marks]

   (b)

   Explain why the disagreement between these two values is a problem for cosmologists, referring to the age and the possible fate of the universe and to dark matter.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A science museum is preparing an exhibition on the expansion of the universe and on the uncertainty over its age and its fate.

   (a)

   Explain how observations of the Doppler shift of light from galaxies are used to show that the universe is expanding.

   [6 marks]

   (b)

   Evaluate how the value of the Hubble constant and the possible existence of dark matter affect conclusions about the age and the ultimate fate of the universe.

   [6 marks]

   Total for question 4: 12 marks

End of questions