SOLUTION: Could you please show me the steps how to solve this problem? The Doppler effect causes a sound moving towards you to sound higher pitched and a sound moving away from you to soun

Question 1181800: Could you please show me the steps how to solve this problem?
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 239 Hz and the stationary frequency was 256 Hz.
Use this information and the equation to estimate the speed of the car in miles/hour, to 1 decimal place.
Found 3 solutions by mananth, MathTherapy, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

c= 761mph
f=239 Hz
f0=256 Hz
(761/239*256)- 761
v= 54.13 mph

Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!

Could you please show me the steps how to solve this problem?
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 239 Hz and the stationary frequency was 256 Hz.
Use this information and the equation to estimate the speed of the car in miles/hour, to 1 decimal place.

I know, for sure, that the answer you're looking for is:
Answer by ikleyn(52804)   (Show Source): You can put this solution on YOUR website!
.

All we need to do is to substitute the given frequencies into equation 239 = . To solve it, cross multiply, simplify and find v 239(761 + v) = 256*761 761 + v = = 815.1 mph v = 815.1 - 761 = 54.1 mph. ANSWER. The speed of the car is 54.1 miles per hour (rounded as requested).

Solved.

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This problem (its TWIN version) was just solved once at this forum under the link

https://www.algebra.com/algebra/homework/equations/Equations.faq.question.1181384.html

https://www.algebra.com/algebra/homework/equations/Equations.faq.question.1181384.html

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