Question #164245

 What is Doppler Effect?

       A police radar set emits a parallel beam of electromagnetic radiation at wavelength λo and velocity c, Which falls on a motor car moving directly towards the set with a velocity u.

       (a.) Derive an expression for the time it takes for the wave front of the radiation initially a distance

       λo from the car, to reach the car.


1
Expert's answer
2021-03-14T19:16:29-0400

The Doppler effect (or the Doppler shift) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source.

fr=ft(1+v/c1v/c)fr=ft(c+vcv)fd=frft=2vftcvfd2vftcf_r=f_t(\frac{1+v/c}{1-v/c}) \\ f_r=f_t(\frac{c+v}{c-v}) \\f_d=f_r-f_t=2v\frac{f_t}{c-v} \\f_d\approx 2v\frac{f_t}{c}

v=λ0tfd2vftc2λ0fttct2λ0ftcfdv=\frac{\lambda_0}{t} \\f_d\approx 2v\frac{f_t}{c}\approx 2\frac{\lambda_0f_t}{tc} \\t\approx 2\frac{\lambda_0f_t}{cf_d}


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