Question

From a vantage point very close to the track at a stock car race, you hear the sound emitted by a moving car. You detect a frequency that is 0.835 times as small as the frequency emitted by the car when it is stationary. The speed of sound is 343 m/s. What is the speed of the car?

Answer 1

Answer:

The speed of the car is 67.77 m/s and it is moving away from the observer.

Explanation:

The apparent frequency is given as

$f' = f\dfrac{ [v - vo]}{ [v - vs]}$

Here

o is the  observer

s is the source which is car

v is the speed of  sound  = 343 m/s

f = true frequency emitted by the car (when stationary)

f ' = 0.835 f

so

$f' = f\dfrac{ [v - vo]}{ [v - vs]}\\0.835 f= f\dfrac{ [v - vo]}{ [v - vs]}\\0.835 = \dfrac{ [343 - 0]}{ [343 - vs]}\\0.835=\frac{343}{343-x}\\x=-67.77 m/s$

The speed of the car is 67.77 m/s and it is moving away from the observer.