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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)f0 , 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 away
was 238 Hz and the stationary frequency was 255 Hz.
Use this information and the equation to estimate the speed of the car in miles/hour, to 1 decimal place.
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As formulated, this text may PERPLEX a student, who reads this description first time in his (or her) life.
For clarity, the formula must be deciphered in two forms
- for approaching source of sound f = , (1)
and
- for receding source of sound f = , (2)
where "v" is the positive MAGNITUDE of the relative velocity.
With the numerical data given at the end of the post, we have case (2) (the car driving away).
So, all we need to do is to substitute the given frequencies into equation (2)
238 = .
To solve it, cross multiply, simplify and find v
238(761 + v) = 255*761
761 + v = = 815.4 mph
v = 815.4 - 761 = 54.4 mph.
ANSWER. The speed of the car is 54.4 miles per hour.
Solved and carefully explained.