# NEET Questions Solved

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

(1) $15.5\text{\hspace{0.17em}}m{s}^{-1},\text{\hspace{0.17em}}200\text{\hspace{0.17em}}Hz$

(2) $19.5\text{\hspace{0.17em}}m{s}^{-1},\text{\hspace{0.17em}}205\text{\hspace{0.17em}}Hz$

(3) $29.5\text{\hspace{0.17em}}m{s}^{-1},\text{\hspace{0.17em}}200\text{\hspace{0.17em}}Hz$

(4) $32.5\text{\hspace{0.17em}}m{s}^{-1},\text{\hspace{0.17em}}205\text{\hspace{0.17em}}Hz$

(3) When train is approaching frequency heard by the observer is

${n}_{a}=n\text{\hspace{0.17em}}\left(\frac{v}{v-{v}_{S}}\right)$$219=n\text{\hspace{0.17em}}\left(\frac{340}{340-{v}_{S}}\right)$ …(i)

when train is receding (goes away), frequency heard by the observer is

${n}_{r}=n\text{\hspace{0.17em}}\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 ${v}_{S}=29.5m/s.$

Difficulty Level:

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