1. 1
   A train travels along a straight track at a constant 30.0 m s⁻¹ with its horn, mounted at the front, sounding at 480 Hz. A person stands beside the track, far enough from it that the train can be treated as moving directly towards and then directly away from her. The speed of sound in air is 340 m s⁻¹ and there is no wind.

   (a)

   What frequency does the person hear as the train approaches?

   [1 mark]

   • A441 Hz
   • B522 Hz
   • C526 Hz
   • D480 Hz

   (b)

   What frequency does the person hear after the train has passed?

   [1 mark]

   • A438 Hz
   • B441 Hz
   • C522 Hz
   • D526 Hz

   (c)

   A passenger sits at the back of the train. State and explain the frequency of the horn that she hears.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   In the laboratory, a sodium absorption line has a wavelength of 589.0 nm. A nearby star is known to be moving directly towards the Earth at 45 km s⁻¹.

   (a)

   At what wavelength is the sodium line observed in the star's spectrum?

   [1 mark]

   • A544.0 nm
   • B588.1 nm
   • C589.1 nm
   • D588.9 nm

   (b)

   Which statement about the Doppler effect for light is correct?

   [1 mark]

   • AOnly the relative velocity of source and observer matters, because light needs no medium
   • BIt occurs only when the source, not the observer, is moving
   • CIt requires the source to move at a speed close to c
   • DIt changes the speed at which the light reaches the observer

   (c)

   Outline why the equation Δλ/λ ≈ v/c is suitable for this star, and why it would not be suitable for an object receding at 0.90c.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A bat flies at 8.0 m s⁻¹ directly towards a large flat wall, emitting ultrasound of frequency 40.0 kHz. It detects the echo from the wall. A second bat, emitting the same frequency and also flying directly towards the wall, detects its echo at 41.2 kHz. The speed of sound in air is 340 m s⁻¹ and the air is still.

   (a)

   Calculate the frequency of the ultrasound received by the wall from the first bat.

   [3 marks]

   (b)

   Determine the frequency of the echo detected by the first bat, and deduce the speed of the second bat.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student compares two situations in still air, where the speed of sound is 340 m s⁻¹. In situation 1, a source emitting 1000 Hz moves at 85 m s⁻¹ directly towards a stationary observer. In situation 2, the source emitting 1000 Hz is stationary and the observer moves at 85 m s⁻¹ directly towards it.

   (a)

   Using wavefronts, explain why the observed frequency increases in each situation, and calculate the frequency heard in each case.

   [6 marks]

   (b)

   Discuss why the two situations give different frequencies for sound but would give the same frequency shift for light. Show that the difference between the two sound situations becomes negligible at low speeds.

   [6 marks]

   Total for question 4: 12 marks

End of questions