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

`4649.20\ \text{Hz}`

Step-by-step explanation:

u = Speed of car = 65 mph

`f_s` = Frequency of source = 24 GHz

c = Speed of light =
`3* 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=(2uf_s)/(c)\\\Rightarrow \Delta f=(2* 65* (1609.34)/(3600)* 24* 10^9)/(3* 10^8)\\\Rightarrow \Delta f=4649.20\ \text{Hz}`

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