A police car is moving at 38.3 m/s (85.7 mi/h) behind a speeding car that is goi

Question

A police car is moving at 38.3 m/s (85.7 mi/h) behind a speeding car that is going faster. The speed limit is 29.1 m/s (65.0 mi/h). A police car radar "clocks" the speed of the other car by emitting microwaves with frequency 3.2 1010 Hz and observing the frequency of the reflected wave. The reflected wave, when combined with the outgoing wave, produces beats at a rate of 1370 s-1. How fast is the speeder going? [Hint: First find the frequency "observed" by the speeder. The electrons in the metal car body oscillate and emit the reflected wave with this same frequency. For the reflected wave, the speeder is the source and the police car is the observer.] Answer in m/s

Explanation / Answer

beat frequency = difference of the two frequencies

1370 = f2 - 3.2 * 10^10

f2 = 32000001370 Hz

by doppler effect

frequency of source = doppler frequency * (speed of wave + speed of observer) / (speed of wave - speed of source)

3.2 * 10^10 = doppler frequency * (3 * 10^8 + v) / (3 * 10^8 - 38.3)

now this frequency will be heard by speeder

so,

3.2 * 10^10 * (3 * 10^8 - 38.3) / (3 * 10^8 + v) = 32000001370 * (3 * 10^8 + 38.3) / (3 * 10^8 - v)

velocity of speeder v = 44.72 m/s

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