Police use radar guns and the Doppler effect to catch speeders. The figure below

Question

Police use radar guns and the Doppler effect to catch speeders. The figure below illustrates a moving car approaching a stationary police car. A radar gun emits an electromagnetic wave that reflects from the oncoming car. The reflected wave returns to the police car with a frequency (measured by on-board equipment) that is different from the emitted frequency. One such radar gun emits a wave whose frequency is 8.0 times 10^9 Hz. When the speed of the car is 25.0 m/s and the approach is essentially head-on, what is the difference between the frequency of the wave returning to the police car and that emitted by the radar gun?

Explanation / Answer

we have to use doppler effect formula

freequency of returning wave= fr= f(V/V-Vc)

   fr= 8x10^9 [344/(344-25)]= 8.63x10^9

so difference in frequencies= fr-f = 8.63x10^9 - 8x10^9 =6.3x10^8 Hz

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