A collection of Doppler effect problems

Here is a set of four problems on the Doppler shift of sound waves. The solutions to the problems are given at the end. If you need a refresher on the Doppler effect, the following note might be useful: How does Doppler effect work?

Question 1

While standing at a crosswalk, you hear a frequency of 560 Hz from an approaching police car. After the police car passes and is moving away from you, you hear a frequency of 480 Hz. What is the speed of the police car (take speed of sound to be v=343 m/s)?

  1. 13.1 m/s
  2. 21.1 m/s
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How does Doppler effect work?

The Doppler effect for sound is a perceived difference between the frequency of sound heard by an observer and the actual frequency emitted by a source, due to relative motion between the source and the observer. A familiar example of this phenomenon is the change in sound frequency of an ambulance or fire engine as it rushes past you. We give a visual explanation of this effect and derive the relation between the observed and emitted frequencies below.

First, recall that the velocity of sound in a medium, v, is a property of the medium alone. That is, after the …

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Doppler effect and beats

JEE Advanced 2019 Paper 1, Question 15

A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When \mathrm{O} is 600 m away from S2 and distance between \mathrm{S} 1 and \mathrm{S} 2 is 800 m, what is the number of beats heard by O?

[Speed of the sound =330 m/s ]

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Recommended reading: How does Doppler effect work?


When there is relative motion between the source and observer, the observed frequency f_o is …

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