Suppose that a police car on the highway is moving to the right at 27 m/s, while

Question

Suppose that a police car on the highway is moving to the right at 27 m/s, while a speeder is coming up from almost directly behind at a speed of 39 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 5.00 109 Hz. (a) Find the magnitude of the difference between the frequency of the emitted wave and the wave that returns to the police car after reflecting from the speeder's car. Hz (b) Which wave has the greater frequency? The wave that returns to the police car has the greater frequency. The emitted wave has the greater frequency. Why?

Explanation / Answer

Let ve = emitter velocity, vr = reflector velocity, +v = receding ve = +26 m/s, vr = -36 m/s f = f0*((c-vr)/(c+ve))*((c-ve)/(c+vr)) = 6800000453.64718 Hz df = f-f0 = 453.64718 Hz (answer)

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