1. 1
   In a laboratory, a hydrogen emission line has a wavelength of 656.3 nm. In the spectrum of light from a distant galaxy, the same hydrogen line is measured at 662.9 nm. Every other line in the galaxy's spectrum is also displaced from its laboratory position.

   (a)

   What can be deduced about the motion of the galaxy relative to Earth?

   [1 mark]

   • AIt is moving towards Earth at about 3.0 × 10⁶ m s⁻¹
   • BIt is moving away at about 1.0 × 10⁻² m s⁻¹
   • CIt is moving away at about 3.0 × 10⁸ m s⁻¹
   • DIt is moving away at about 3.0 × 10⁶ m s⁻¹

   (b)

   A different line has a laboratory wavelength of 486.1 nm. At what wavelength is it observed in the galaxy's spectrum?

   [1 mark]

   • A491.0 nm
   • B479.5 nm
   • C481.2 nm
   • D492.7 nm

   (c)

   Explain why astronomers can be confident that the displacement is caused by the galaxy's motion rather than by the galaxy containing different elements.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   An ambulance travels at constant speed along a straight road with its siren sounding at a frequency of 700 Hz. A cyclist is waiting at the side of the road some distance ahead of the ambulance.

   (a)

   As the ambulance approaches, what does the cyclist hear?

   [1 mark]

   • AA frequency lower than 700 Hz
   • BA frequency of 700 Hz, but louder
   • CA frequency higher than 700 Hz
   • DA higher frequency, because the speed of sound increases in front of the ambulance

   (b)

   Which statement describes the wavefronts of the siren in front of the moving ambulance?

   [1 mark]

   • AThey are closer together than behind it, and travel faster
   • BThey are closer together than behind it, and travel at the same speed
   • CThey are further apart than behind it, and travel at the same speed
   • DThey are equally spaced all round, but the siren vibrates faster

   (c)

   The ambulance stops, still sounding its siren, and the cyclist then rides towards it. Explain why she hears a frequency above 700 Hz even though the wavefronts are now evenly spaced.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A police speed gun emits microwaves of frequency 24.0 GHz towards a car that is driving directly towards it. The microwaves reflected from the car return to the gun with a frequency 3.20 kHz higher than the emitted frequency. The speed limit on the road is 70 km h⁻¹.

   (a)

   Explain why the change in frequency of the reflected microwaves is approximately twice the change that a detector fixed to the car would measure.

   [3 marks]

   (b)

   Determine the speed of the car and evaluate whether the evidence shows that the driver is breaking the speed limit.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An astronomer observes a star that has an unseen companion. Over many nights, the hydrogen line whose laboratory wavelength is 656.28 nm is seen to shift smoothly back and forth, between a shortest wavelength of 656.17 nm and a longest wavelength of 656.39 nm, repeating every 12.0 days. The wavelength midway between these extremes is equal to the laboratory value.

   (a)

   Explain what these observations show about the motion of the star, and determine its maximum speed along the line of sight.

   [6 marks]

   (b)

   Evaluate the claim that this method gives the true orbital speed of the star. In your answer, consider whether the approximation used to calculate the speed is valid.

   [6 marks]

   Total for question 4: 12 marks

End of questions