Question #164249

          

 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.λo from the car, to reach the car.

 (a Derive an expression for the wavelength λ of the radiation reflected from the car

(b) If Zo = 0 im, c = 3.0 × 108ms'1 and u = 33ms'1, calculate the change in wavelength of tho

    radiation received at the set after reflection from the car. 


1
Expert's answer
2021-03-16T08:31:38-0400

Given quantities: λo\lambda_o cc uu

The beat frequency between a microwave transmitted signal and a reflected signal of a moving object is

freflectedftransmitted=Δf=2νtargetcff_{reflected} - f_{transmitted} = \Delta f = \large\frac{2\nu_{target}}{c}f

where the target velocity is taken as positive if the target if approaching the transmitter. Police RADAR uses this method for measurement of auto speed.

Δff=2uc\large\frac{\Delta f}{f} = \frac{2u}{c}

λλ0=2ucλ=2ucλo\large\frac{\lambda}{\lambda_0} = \frac{2u}{c} \to \lambda = \large\frac{2u}{c}\lambda_o


2) λλ0=2uc=2331033108=\large\frac{\lambda}{\lambda_0} = \frac{2u}{c} = \frac{2*33*10^{-3}}{3*10^8} = 22101122*10^{-11}


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