How Does Speed Affect Radar Frequency Shift?

[akan]

Homework Statement

What is the frequency shift of a 72 GHz police radar signal when it reflects off a car moving at 111 km/h? (Radar waves travel at the speed of light = 340 m/s.)

--------
f' = f(1 +- u/v) (moving observer, + appr, -receding)
f' = f/(1 +- u/v) (moving source, - appr, +receding)
--------

f = 72 GHz = 72 * 10^9 Hz.
u = 111 * 10^3 / 3600 m/s
v = 340 m/s

f' = f(1+u/v)
f'' = f(1+u/v)/(1-u/v)
f'' = (72 * 10^9 Hz)(1+(111 * 10^3 / 3600 m/s)/340)(1-(111 * 10^3 / 3600 m/s)/340)

Calculating this formula does not give the correct result. What am I doing wrong?

 

[Redbelly98]

The speed of light is actually a lot larger than 340 m/s. It seems you're using the speed of sound instead.

 

[akan]

Wow, that is probably the reason. The whole chapter was on sound so I thought the problem was, too, and didn't read it correctly. Did I make any other mistakes? Thanks.

 

[Redbelly98]

I don't remember the exact formulas and don't have them handy, I just spotted the velocity error so I posted.