The Doppler Effect

[Outc4sted]

1. The problem statement, all variables and given/known data

You are in charge of calibrating the radar guns for a local police department. One such device emits microwaves at a frequency of 2.15 GHz. During the trials, these waves are reflected from a car moving directly away from the stationary emitter. You detect a frequency difference (between the received microwaves and the ones sent out) of 291 Hz. Find the speed of the car and give the answer in km/h.

2. Relevant equations

http://ebooks.bfwpub.com/physse6e/figures/EQ_15_41a.jpg

3. The attempt at a solution

One thing that I kind of don't understand, is that the radar gun is both the emitter and receiver, and the guy is stationary. So I just assumed that you would treat the car as the receiver. I even attempted to treat the car as the emitter and the guy as the receiver thinking of after the microwaves hit the car, but that gave the same answer.

(2.15 * 10^9 ) - 291 = ( (343 - v)/(343) ) * (2.15 * 10^9 )

v = 4.6425 * 10^-5 m/s
v * 3.6 = 1.6 * 10^-4 km/h

[ideasrule]

Radar guns use microwaves, not sound, and they travel at 300 million meters per second. Much faster than the 343 m/s you were using.

[CFDFEAGURU]

Think it through. The gun is stationary. The car is moving.

[ideasrule]

Also, there are two sources of redshift:

(1) The radar gun's microwaves hit the car, which perceives them to be redshifted Here, the radar gun is the emitter and the car is the receiver.
(2) The car reflects the microwaves back at the frequency it believes them to be at. Since the gun is moving away, the microwaves are redshifted a second time. Here, the car is the emitter and the car is the receiver.