A tuning fork measured by a police radar gun

[kostoglotov]

A police radar gun emits radio waves at 10.5 GHz, and measures the beats between this frequency and the returned waves to determine the speed of an object.

It registers a tuning fork as "traveling" at 24.6 m/s. What is the frequency of the tuning fork.

I can get the answer, but I don't understand why it's the answer.

I used the formula for change in frequency of reflected waves seen here:

link: http://i.imgur.com/PStzkdj.gif

It gives the correct answer as per the back of the text, if you plug in all the relevant variables. I kind of just guessed at using that formula, because it's the only one where the available variables fit the information the question gives.

Now I understand, that from the POV of the light waves, the tuning fork is moving very slowly, and that while the tuning fork is swaying in one direction, millions of light waves have the chance to hit and reflect off the fork. So I can understand how the tuning fork being hit by the radio waves can cause a shift in the frequency of the reflected waves.

But why is the shift in the frequency of the reflected radio waves the same as the frequency of the tuning fork?

 

[mfb]

The amplitude of the oscillation of the tuning fork is significantly smaller than 1 wavelength. All you get is a phase shift that oscillates around some unknown central value with the frequency of the tuning fork. The interference signal will probably (depending on where the central phase is) also oscillate with this frequency, which could get interpreted using the formula you posted.