Understanding the Relativistic Doppler Effect for Police Radar Technology

[andrew410]

More specifically the problem deals with the relativistic doppler effect.

Police radar detects the speed of a car. Microwaves of a precisely known frequency are broadcast toward the car. The moving car reflects the microwaves with a Doppler shift. The reflected waves are received and combined with an attenuated version of the transmitted wave. Beats occur between the two microwave signals. The beat frequency is measured.
(a) For an electromagnetic wave reflected back to its source fomr a mirror approaching at speed v, show that the reflected wave has a frequency:
$$f = f_{source}\frac {c+v}{c-v}$$

I'm not sure how they got this. I know that the beat frequency is the reflected frequency minus the transmitted frequency, but don't understand how to apply it to the given formula in my book. The given formula in the book is:
$$f_{obs} = \frac{\sqrt{1+\frac{v}{c}}}{\sqrt{1-\frac{v}{c}}} f_{source}$$

I did simplify the given formula in order to get:
$$f_{obs}^2 = \frac{c+v}{c-v} f_{source}^2$$

I don't know what to do from here. Please help...any help will be greatly appreciated. Thx in advance! :)

 

[robphy]

When does one apply the doppler shift?
How many "doppler shifts" occur in this problem?

 

[andrew410]

One applies the doppler shift to find the shift in frequency because of time dilation.
Not sure how many doppler shifts occur though...1?

 

[OlderDan]

One applies the doppler shift to find the shift in frequency because of time dilation.
Not sure how many doppler shifts occur though...1?

If the car itself was generating the microwaves there would be a doppler shift analogous the dopler shift of a car making a sound. In this case the car is not generating the microwaves, it is reflecting the waves it receives that were generated ba a source that from the car's point of view is moving toward it. Look at it from the rest frame of the car and decide what frequency waves are leaving the car after reflection. Then look at the receiving end of those reflected waves.