First slide

Doppler

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

Moderate

A

$15.5 {ms}^{- 1}, 200 Hz$
B

$19.5 {ms}^{- 1}, 205 Hz$
C

$29.5 {ms}^{- 1}, 200 Hz$
D

$32.5 m s^{- 1}, 205 H z$

Solution

When train is approaching frequency heard by the observer is
$n_{a} = n (\frac{v}{v - v_{S}}) \Rightarrow 219 = n (\frac{340}{340 - v_{S}}) (i)$
when train is receding (goes away), frequency heard by the observer is
$n_{r} = n (\frac{v}{v + v_{s}}) \Rightarrow 184 = n (\frac{340}{340 + v_{s}}) (ii)$
On solving equation (i) and (ii) we get n = 200 Hz and $v_{s} = 29.5 m / s$

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