The Doppler Effect
4 marks · NormalA police car moves directly towards a stationary observer at a speed of 30 m/s. The siren emits a sound with a frequency of 800 Hz. The speed of sound in air is 340 m/s.
Explain why the observer hears a higher frequency as the car approaches.
Calculate the observed frequency of the siren heard by the observer. Give your answer to 2 significant figures.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) Waves are compressed as the car approaches, so the observer hears a higher frequency.
(b) Observed frequency = 873 Hz
Common mistakes: Forgetting to use correct Doppler formula.; Not rounding to 2 significant figures.
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Explains higher frequency is due to compression of waves as the source approaches.
M1 (b) · 1 mark · States or uses correct Doppler effect formula: (where source moves towards observer).
M2 (b) · 1 mark · Correct substitution: .
A1 (b) · 1 mark · Final answer 873 Hz, to 2 sig. figs: 870 Hz (accept 873 Hz).
Worked solution
(a) As the police car moves towards the observer, the sound waves in front are compressed, causing an increase in frequency (higher pitch) heard by the observer.
(b) Use the Doppler effect formula for a source moving towards a stationary observer:
where:
- f = 800 Hz (emitted frequency) - v = 340 m/s (speed of sound) - v_s = 30 m/s (speed of source towards observer)
To 2 significant figures: 870 Hz.