As shown in the figure, a man is traveling on a bicycle along a straight road th

Question

As shown in the figure, 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 10 m/s, he hears the whistle of a train that is behind him, as shown in the figure. 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

Given : velocity of man = 10 m/s

Frequency heated by man = 774 Hz

Frequency emitted by train = 820 Hz

Speed of sound = 340 m/s

Solution :

(b)

fL = [(v+vL)/(v+vs)].fs

774= [ (340-10)/(340+vs) ].820

vS = 9.61 m/s, away from bicycle .

(a)

Using the same equation :

fL= [(340+0)/(340+9.61)].820

= 797.46 Hz

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