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

Question

A man traveling on a bicycle along a straight road that runs parallel to and right next to some railroad tracks. While moving at 10 m/s, he hears the whistle of a train that is behing him. The frequency emitted by the train's whistle is 820 Hz, but the frequency the man hears is 774 Hz. The speed of sound is 340 m/s.

A.) What frequency is heard by a 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)

Frequency heard by man on bicycle ; f =  [(c-Vm)/(c+Vt)]*fo

Frequency heard by stationalry man, f' =  [c/(c+Vt)]*fo

So, f/f' = (c-Vm)/c = 1-Vm/c

So, 774/f' = 1 - 10/340

So, f' = 797.5 Hz <---------answer

B)

Frequency heard , f = [(c-Vm)/(c+Vt)]*fo

where Vm = velocity of man = 10 m/s

Vt = velocity of train

c = velocity of sound in air = 340

As the observed freqiency is less than emitted frequency, so the sign of Vm is -ve and Vt is +ve so as to make (f < fo) which means that the train is moving away from the bicycle <-------answer

So, 774 = [(340-10)/(340+Vt)]*820

So, Vt = 9.61 m/s <--------answer

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