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A man standing on a platform observes that the frequency of the sound of a whistle emmited by a train drops by 140Hz .if the velocity of sound in air is 330m/s and speed of the train is 70m/s ,the frequency of the whistle is?

A man standing  on a platform observes that the frequency of the sound of a whistle emmited by a train drops by 140Hz .if the velocity of sound in air is 330m/s and speed of the train is 70m/s ,the frequency of the whistle is?
 

Grade:11

1 Answers

Arun
25750 Points
5 years ago
This question is based on Doppler Effect. 
We can write a formula for apparent frequency (f'),when the source (train) is moving away from the observer (man).
f' = (V X f) / (V + u)
f' = Apparent frequency
V= velocity of sound in air = 330 m/s
f = real frequency
u = velocity of source= 70 m/s
Now we can substitute above values in to the formula,
f' = (330f)/(330+70) = 330f/400 =33f/40 ------- (1)
but we know that, real frequency - apparent frequency = 140 Hz
f  - f' = 140
by equation (1 ),  f - (33f/40) = 140
7f/40 = 140
f = 140 X 40/7
frequency of the whistle = f =800 Hz

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