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 0.86 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

55.8 m/s

Step-by-step explanation:

`f` = Actual frequency of sound emitted by car

`f'` = frequency observed when the car moves =
`(0.86)f`

`V` = Speed of sound = 343 m/s

`v` = Speed of car

Frequency observed is given as

`f' = (Vf)/(V+v)`

`(0.86) = ((343))/(343 + v)\\(0.86) = ((343))/(343 + v)\\294.98 + (0.86) v = 343 \\v = 55.8 ms^(-1)`