Suppose that a police car on the highway is moving to the right at 29 m/s, while

Question

Suppose that a police car on the highway is moving to the right at 29 m/s, while a speeder is coming up from almost directly behind at a speed of 33 m/s, both speeds being with respect to the ground. The police officer aims a radar gun at the speeder. Assume that the electromagnetic wave emitted by the radar gun has a frequency of 8.00 109 Hz. Find the the difference between the frequency of the wave that returns to the police car after reflecting from the speeder's car, and the original frequency emitted by the police car.

a) _________Hz

b) The emitted wave has the greater frequency. OR The wave that returns to the police car has the greater frequency.

Explanation / Answer

The relative speed u is 33 - 29 = 4 m/s
The difference in frequency between the emitted wave and the reflected wave = 2*f*(u/c)
= 2* 8.0 * 10^9 * (4/(3*10^8))
= 213.3 Hz

(b)
The cars are approaching each other, so the Doppler shifted frequency will be greater.
The wave that returns to the police car has the greater frequency.

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