A highway police radar operating at 10 GHz observes a Doppler shift of 1,500 Hz when the radar is pointed at a moving car. What is the radial speed of the car toward the radar in miles per hour?
A radar emits waves. The waves reflect from a barrier (the car). Since the car moves, the incident waves reflect with some additional shift, which causes Doppler shift.
"f=f_0\\bigg(1+\\frac vc\\bigg), [f>f_0]\\\\\\space\\\\\nv=\\frac{c(f-f_0)}{f_0}=\\frac{c\\Delta f}{f_0},\\\\\\space\\\\\nv=\\frac{3\\cdot10^8\\cdot1500}{10\\cdot10^9}=45\\text{ m\/s}."
45 m/s is 162 km/h.
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