A man is traveling on a bicycle along a straight road that runs parallel to and

Question

A man is traveling on a bicycle along a straight road that runs parallel to and right next to some railroad tracks. While moving at 10m/s, he hears the whistle of a train that is behind him. The frequency emitted by the train's whistle is 820Hz, but the frequency the man hears is 774Hz. The speed of sound is 340m/s. A) What frequency is heard by the stationary observer located between the train and the bicycle? B) What is the speed of the train, and is the train traveling away from or toward the bicycle?

Explanation / Answer

A)

with reference to the given data

Vr is the velocity receiver is = -10m/s,

Vs is source velocity

V is the sound velocity in air is or speed of sound is 340m/s.

f is freqeuncy a man hears 774 Hz

Fo is the original frequency = 820 Hz

we have a equation with frequency is f = Fo X ( V + Vr ) / ( V + Vs )

774 = 820 X ( 340 - 10 ) / ( 340 + Vs)

( 340 + Vs) = 820 X 330 / 774

( 340 + Vs) = 349.612

Vs = 349.612 - 340

Vs = 9.612 m / s

B )

f = Fo X ( V + Vr ) / ( V + Vs )

f = 820 X ( 340 + 0 ) / ( 340 - 9.612 )

f = 278800 / 330.388

f = 843.856 Hz

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