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 31 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.(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.
1 Hz
(b) Which wave has the greater frequency?

Why?

Explanation / Answer

(a).Let ve = emitter velocity, vr = reflector velocity, +v = receding

ve = +29 m/s, vr = -31 m/s

f = f0*((c-vr)/(c+ve))*((c-ve)/(c+vr))

= (8.0*10^9)[[(3*10^8-(-31))/(3*10^8+29)] * [(3*10^8-29)/(3*10^8+(-31)]

= 8000000107 Hz

df = f-f0 = (8000000107) - (8.0*10^9) = 106.666 Hz 106.7 Hz

(b).

The cars are approaching each other, so the emitter waves are ``blue shifted'', that is the Doppler

shifted frequency will be greater.

so,emitted wave has the greater frequency

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