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 police radar transmits at a frequency of 24.0 GHz and receives a wave reflected from a car moving toward the radar at 65.0 mph. Find the frequency shift Df 5 fO 2 fS between the observed (received) and source (transmitted) frequencies.

Answer 1

Answer:

$4649.20\ \text{Hz}$

Explanation:

u = Speed of car = 65 mph

$f_s$ = Frequency of source = 24 GHz

c = Speed of light = $3\times 10^8\ \text{m/s}$

Beat frequency or frequency shift between the observed (received) and source (transmitted) frequencies is given by

$f_o-f_s=\dfrac{2uf_s}{c}\\\Rightarrow \Delta f=\dfrac{2\times 65\times \dfrac{1609.34}{3600}\times 24\times 10^9}{3\times 10^8}\\\Rightarrow \Delta f=4649.20\ \text{Hz}$

The difference between te required frequencies is $4649.20\ \text{Hz}$.