Calculating Relativistic Doppler Shift for Moving Radar

[fluidistic]

Homework Statement

A car is getting closer to a radar as a speed of 135 km/h. If the radar works at a 2 \times 10 ^{9} Hz, what difference of frequency is observed for the radar?

Homework Equations

\mu=\frac{\mu _0 \sqrt {1- \frac{v^2}{c^2}}}{1-\frac{v}{c}}

The Attempt at a Solution

I converted 135 km/h into m/s, which gave me \frac { 1350 m }{36 s}.
Then I applied the formula and \mu - \mu _0 gave me 1.024 \times 10^{13} Hz which seems WAY too big to be realistic. Am I missing something? Is it a wrong formula?!

 

[kuruman]

The formula is correct and I agree the number is way too large. Can you show how you got it? A word of caution: v/c is too small to plug in a calculator and expect something other than μ₀, i.e. no frequency shift. I suggest that you try a Taylor expansion for small values of v/c.