How Does the Doppler Effect Alter Radar Frequencies?

[Lengalicious]

Homework Statement

Radar is used to measure the speed of passing vehicles. A stationary radar gun emits EM radiation, a proportion of which is reflected from the target vehicle which is moving away from the gun at 'u' ms^-1.

a)State the frequency at the target vehicle (f.tar) in terms of the frequency at the radar gun (f.sou).

The target vehicle then acts as a moving source emitting at frequency (f.tar), moving away from the radar gun.

b) State the frequency of the reflected radiation (f.ref) at the radar gun in terms of the frequency reflected by the target vehicle (f.tar).

c) Combine these expressions to relate the initial frequency (f.sou) to the reflected frequency (f.ref), simplifying the expression by assuming u<<c.

Homework Equations

The Attempt at a Solution

I say f.tar = ((c-u)/c)*f.sou
and f.ref = (c/(c+u))*f.tar

so, f.ref = (c/(c+u))*((c-u)/c)*f.sou

where f.ref = f.sou when u<<c. This surely can't be correct? What am i doing wrong?? Apparently there should be a beat frequency =S

 

[flatmaster]

where f.ref = f.sou when u<<c. This surely can't be correct? What am i doing wrong?? Apparently there should be a beat frequency =S

Why is this incorrect? In the case that u=0, you would expect f.ref = f.sou. If there's no relative velocity there is no doppler shift.