A train is moving parallel and adjacent to a highway with a constant speed of 24

Question

A train is moving parallel and adjacent to a highway with a constant speed of 24 m/s. A car is traveling in the same direction as the train at 52 m/s. The car's horn sounds at 510 Hz and the train's whistle sounds at 380 Hz. When the car is behind the train what frequency does an occupant of the car observe for the train whistle? The speed of sound is 343 m/s. Answer in units of Hz. When the car is in front of the train what frequency does a train passenger observe for the car's horn? Answer in units of Hz.

Explanation / Answer

from the given data

v_train = 24 m/s

v_car = 52 m/s

f1 = 510 hz

f2 = 380 hz

v = 343 m/s

1) the frequency heard by obsorver in the car,

f2' = f2*(v + v_car)/(v - v_tarin)

= 380*(343 + 52)/(343 - 24)

= 470.5 Hz

2)

the frequency heard by obsorver in the train,

f1' = f1*(v + v_train)/(v - v_car)

= 510*(343 + 24)/(343 - 52)

= 643.2 Hz

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