Question

Police radar guns measure the speed of moving vehicles by transmitting electromagnetic waves at a vehicle and detecting a Doppler shift in the reflected wave. Suppose a police radar transmits at a frequency of 25 GHz and receives a wave reflected from a car moving toward the radar at 50 m/s. Find the frequency shift observed by the radar gun after it is reflected off of the approaching car.

Answer 1

8333.33 Hz.

Step-by-step explanation:

f = Transmitted frequency = 25 GHz = 25×10⁹ Hz

v = Velocity of car = 50 m/s

c = Speed of light = 3×10⁸ m/s

Frequency shift

`\Delta f=(2fv)/(c)\\\Rightarrow \Delta f=(2* 25* 10^9* 50)/(3* 10^8)\\\Rightarrow \Delta f=8333.33\ Hz`

∴ Frequency shift or beat frequency observed is 8333.33 Hz.