# HEY YOU! Double Doppler/Radar Guns/Equation Derivation

Alright. Physics Internal. I am investigating a physics principle applied into a practical way. Radar Guns and the Doppler Effect. Now the issue is, firstly, that I have encountered two equations to give me the perceived frequency of a wave with a moving observer and stationary source. I am not sure if they are one and the same.
Here they are:
f' = (c+Vr/c) x f
and
f' = f (1 + Vr/c)

Vr = velocity of moving observer
c = velocity of wave
fi = perceived frequency.

My last issue, is that i have examined the physics behind the double doppler effect, this is the principle the radar gun works on. However what I need to know is how the radar gun turns the changed frequency it receives back (from the object it is trying to calculate speed of) into calculating the speed of the object? How would i derive this equation?

Many Thanks
Jamie

## The Attempt at a Solution

mfb
Mentor
I am not sure if they are one and the same.
Here they are:
f' = (c+Vr/c) x f
and
f' = f (1 + Vr/c)
You can check the units - they do not match in one of those equations. Units in correct equations always match.

My last issue, is that i have examined the physics behind the double doppler effect, this is the principle the radar gun works on. However what I need to know is how the radar gun turns the changed frequency it receives back (from the object it is trying to calculate speed of) into calculating the speed of the object? How would i derive this equation?
Assume that that the receiver (the car) emits the same frequency again, and calculate the frequency the initial emitter (the radar gun) receives. You can solve this formula for the velocity.

The first equation is not correct, unless you intended to write ## f' = \frac {c + V_r} {c} f ##, when it is equivalent to the correct second equation.

I am unsure what you are asking about, though. Do you need to know how this equation is derived?