How would you solve this physics problem on relativity and the doppler effect?

[amr55533]

Homework Statement

Police radar detects the speed of a car as follows: Microwaves of a precisely known frequency are broadcast toward the car. The moving car reflects the waves with a doppler shift. The reflected waves are received and combined with an attenuated version of the tansmitted wave. Beats occur between the two microwave signals. The beat frequency is measured.

a) For an electromagnetic wave reflected back to its source from a mirror approaching at speed v, show that the reflected wave has a frequency: f=fsource[(c+v)/(c-v)]

b) When v is much less than C, the beat frequency is much smaller than the transmitted frequency. In this case use the approximation f+fsource=2fsource and show that the beat frequency can be written as:

fbeat=2v/(lambda)

I figured out part A, but I am unsure how to derive part B.

Thanks!

Homework Equations

f=fsource[(c+v)/(c-v)]

f=fsource=2fsource

f*(lambda)=C

The Attempt at a Solution

For part A, I simply applied fobs=fsource[sqrt(1+v/c)]/[sqrt(1-v/c)] twice, where the mirror would be the first observer. I am just unsure on part B.

 

[haruspex]

I don't see how the approximation suggested helps (or that it is valid), but you should be able to simplify [sqrt(1+v/c)]/[sqrt(1-v/c)] based on v << c. Use the binomial expansions.

 

[voko]

What is the equation for beat frequency?