(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A radar "speed gun" emits microwaves of frequency f_{o}=36.0 GHz. When the gun is pointed at an object moving toward it at speed v, the object senses the microwaves at the Doppler-shifted frequency f. The moving object reflects these microwaves at this same frequency f. The stationary radar apparatus detects these reflected waves at a Doppler-shifted f'. The gun combines its emitted wave at f_{o}and its detected wave at f'. These waves interfere, creating a beat pattern whose beat frequency is f_{beat}=f'-f_{o}.

a.) Show that: v≈cf_{beat}/2f_{o},

if f_{beat}<<f_{o}. If f_{beat}=6670 Hz, what is v(km/h)?

b.) If the object's speed is different by v, show that the difference in in beat frequency Δf_{beat}is given by : Δf_{beat}=2f_{o}Δv / c

c.) If the accuracy of the speed gun is to be 1 km/h, to what accuracy must the beat frequency be measured?

2. Relevant equations

f=c/λ = f_{o}[(c+v/c-v)^1/2]

λ=λ_{o}[(c-v/c+v)^1/2]

1/f_{o}=λ_{o}/c

3. The attempt at a solution

I am kind of lost on this problem, I think I heard my teacher say I'd need a double doppler shift. Any help and hints are appreciated!

Thanks

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# Doppler-shifted frequency problem

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