Use this information and the equation to estimate the speed of the car in miles/hour, to 1 decimal place.

Question

The Doppler effect causes a sound moving towards you to sound higher pitched and a sound moving away from you to sound lower pitched, like observed in listening to the car horn in the video.

The equation for this is f = (c/(c+v))f_0, where
f is the observed frequency (pitch) of the sound, in Hertz
c is the speed of sound, about 761 miles per hour,
v is the speed of the sound source, in this case the car, in miles per hour
f0 is the frequency of the sound when stationary

Using a spectrum analyzer, we could determine the observed frequency when the car was driving towards us was 267 Hz and the frequency while driving away was 241 Hz, suggesting a stationary frequency of 254 Hz.

Answer 1

Sha,

 

You've described the problem nicely, provided the equation and the data, so what is your difficulty in solving the equation for v?

 

Rewriting your formula, v = c [ (f_o/f) - 1]

v = 761 mph [(254/241) - 1] = 761 (0.05394) = 41.05 mph

 

NOTE.  Because your formula had (c + v) in it, you have to use the f = 241 Hz frequency (while driving away case).