Q. 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
A) $15.5\ ms^{- 1},200Hz$
B) $19.5\ ms^{- 1},205Hz$
C) $29.5\ ms^{- 1},200Hz$
D) $32.5\ ms^{- 1},205Hz$
Explanation
(c) When train is approaching frequency heard by the observer is
$n_{a} = n\left( \frac{v}{v - v_{S}} \right) \Rightarrow 219 = n\left( \frac{340}{340 - v_{S}} \right)$ …(i)
When train is receding (goes away), frequency heard by the observer is
$n_{r} = n\left( \frac{v}{v + v_{S}} \right) \Rightarrow 184 = n\left( \frac{340}{340 + v_{S}} \right)\ $ …(ii)
On solving equation (i) and (ii) we get $n = 200Hz$ and $v_{S} = 29.5m/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.