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andrew410

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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:

[tex] f = f_{source}\frac {c+v}{c-v} [/tex]

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:

[tex] f_{obs} = \frac{\sqrt{1+\frac{v}{c}}}{\sqrt{1-\frac{v}{c}}} f_{source}[/tex]

I did simplify the given formula in order to get:

[tex] f_{obs}^2 = \frac{c+v}{c-v} f_{source}^2[/tex]

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