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 0.855 times smaller than that 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

apparent frequency
n' = n [v - vo] / [v - vs]
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o >> observer, s >> source (car), v = sound speed = 343 m/s
n = true freq emitted by car (when stationary)
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No where it is given that "car is receding away" (as presumed by Mr Bekki above) >>> the fact that apparent frequency heard by the observer id "smaller" which indicates the status or ARROW of car. still, let the formula return it with sign
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in above COMPOSITE formula >>> it is a must that all Vo, Vs, V move in ONE direction (say + x) if any one is not in same sense then it must be resolved along.

let observer be at ORIGIN (vo=0)
sound is coming towards observer>> v = +343
vs = + ve here in formula, lets see how given n' dictates
n ' = 0.855 n
so
0.855 = [v - 0] / [v - vs]
855 (v - vs) = 1000 v
- 855 vs = 115 v
vs = - 115*343/855 = - 46.13 m/s
negative sign indicates that car is moving in (- x) direction or is receding away from observer.

Hope It will help you. please rate the answer.