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
Diffcult
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(c) When train is approaching frequency heard by the observer is
${n_a} = n\,\left( {\frac{v}{{v - {v_S}}}} \right)$
$⇒$ $219 = n\,\left( {\frac{{340}}{{340 - {v_S}}}} \right)$ …$(i)$
when train is receding (goes away), frequency heard by the observer is
${n_r} = n\,\left( {\frac{v}{{v + {v_s}}}} \right)$
$⇒$ $184 = n\left( {\frac{{340}}{{340 + {v_s}}}} \right)$ …$(ii)$
On solving equation $(i)$ and $(ii)$ we get $n = 200Hz$
and ${v_S} = 29.5m/s.$
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