An alert physics student stands beside the tracks as a train rolls slowly past. He notes that the frequency of the train whistle is 491 Hz when the train is approaching him and 472 Hz when the train is receding from him. Using these frequencies, he calculates the speed of the train. What value does he find? (Assume the speed of sound in air is 343 m/s.)

6.73

Explanation:

When the train is approaching

f = 491

491 = f (s) [ v / (v - v (s)) ]

When the train is receding,

f = 472

472 = f (s) [ v / (v + v (s)) ]

next, we divide the frequency when the train is approaching by the frequency when the train is receding. Thus,

491 / 472 = [v + v (s) ] / [v - v (s) ]

1.04 = [v + v (s) ] / [v - v (s) ], where

v = 343 m/s

v (s) = speed of train

1.04 = [343 + v (s) ] / [343 - v (s) ]

356.72 - 1.04v (s) = 343 + v (s)

356.72 - 343 = v (s) + 1.04v (s)

13.72 = 2.04v (s)

v (s) = 13.72 / 2.04

v (s) = 6.73 m/s