If you are cruising down the road at 50 mph and a policeman with a radar gun (wa

Question

If you are cruising down the road at 50 mph and a policeman with a radar gun (wavelength 1 cm) reflects radar light off your bumper, what wavelength of radar light does he get back? Assume the policeman is stationary, and you are moving towards him. Light that gets reflected has twice as much shift as light that is just emitted, so use the formula for the shift of emitted light but multiply by two. (Hint: convert mph to m/s)

Explanation / Answer

50mph = 22.35200 m / s In classical physics, where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, the relationship between observed frequency and emitted frequency is given by: f = [(c+vr) / (c+vs)]* f0 where c is the velocity of waves in the medium; vr is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source (and negative in the other direction); vs is the velocity of the source relative to the medium; positive if the source is moving away from the receiver (and negative in the other direction) therefore: f = [334/ (334+22.35200) ]* f0 => f/f0 = 0.9372 W1f1 = W2 f2 , where w is the wavelength => 1*f0/f = w2 => w2 = 1/ 0.9372 => w2 = 1.067 cm_________________________________________answer

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