# Beats + Doppler effect : How do radar guns work?

Concepts involved:

Doppler Effect and Beats

Radar stands for RAdio Detection And Ranging. The way radar guns work to find out the speed of an object is that a high frequency radio wave is transmitted from the gun onto the object whose speed you would like to measure.

This wave bounces off the moving object and then returns back to the radar gun. A circuit in the gun amplifies the signals and adds them together.

Case – I

Let’s consider a stationary object. Any wave that hits the object reflects back and get back to you in the same frequency. If you add these signals up you would get a wave with the following amplitude:

$y(t) =\sin(2 \pi f t) + \sin(2 \pi f t + \phi)$

Case-II

Now if that object is moving with some velocity, your reflected wave would be doppler shifted. This means the frequency of the received wave is different than the transmitted wave. And when you add those two signals up you get:

$y = sin(2 \pi f t) + sin(2 \pi f_1 t) \rightarrow \text{Beats Phenomenon}$

$f_{beats} = | f - f_1 |$

Since each velocity corresponds to a particular beat frequency, radar guns use the beat frequency as a measure to find out how fast an object is moving.