Memoirs of Fls'Zen

Saturday, June 18, 2011

Doppler Effect

Have you ever wondered how fast that car is driving when it speeds by your house late at night? I have. Of course, Wikipedia's Doppler Effect article isn't very helpful with this specific question. Oh well.

If we make an audio recording of the vehicle driving by, we can perform spectrum analysis on it and determine the change in frequency as it drives by. Pick a clean doppler shift from the spectrum graph and call the higher frequency "h" and the lower "l". Let's also call the speed of sound "v". Now, we can evaluate:

s = v(h-l)/(h+l), where s is the speed of the car. Wasn't that easy!?! Of course, this is for the observer remaining still.

So, how did I arrive at that? A little algebra. Let's call the frequency the car is generating (the one we picked the high and low for) "f". If we solve the doppler equation for "f", and split it into two equations, one for the high frequency and one for the low, we end up with:

f = h(v-s)/v
f = l(v+s)/v

Now, set the right hand parts equal to each other:

h(v-s)/v = l(v+s)/v

And, solve for s:

s = v(h-l)/(h+l).

Now, I just have to write spectrum analyzer software to detect good doppler shifts and automatically produce the result. Maybe an iOS app?



Post a Comment

Subscribe to Post Comments [Atom]

<< Home