wave_mechanics dopplers_effect Question 32
Question: An observer standing at station observes frequency 219 Hz when a train approaches and 184 Hz when train goes away from him. If velocity of sound in air is 340 m/s, then velocity of train and actual frequency of whistle will be
[RPET 1997]
Options:
A) $ 15.5m{{s}^{-1}},\ 200Hz $
B) $ 19.5m{{s}^{-1}},\ 205Hz $
C) $ 29.5m{{s}^{-1}},\ 200Hz $
D) $ 32.5m{{s}^{-1}},\ 205Hz $
Show Answer
Answer:
Correct Answer: C
Solution:
When train is approaching frequency heard by the observer is $ n _{a}=n( \frac{v}{v-v _{S}} ) $
Therefore $ 219=n( \frac{340}{340-v _{S}} ) $ ?(i) when train is receding (goes away), frequency heard by the observer is $ n _{r}=n( \frac{v}{v+v _{s}} ) $
Therefore $ 184=n( \frac{340}{340+v _{s}} ) $ ?(ii) On solving equation (i) and (ii) we get $ n=200Hz $ and $ v _{S}=29.5m/s.
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