The apparent frequency of a note, when a listener moves towards a stationary source, with velocity of $40 m/s$ is $200 Hz$. When he moves away from the same source with the same speed, the apparent frequency of the same note is $160 Hz$. The velocity of sound in air is (in $m/s$)
A$360$
B$330$
C$320$
D$340$
Medium
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A$360$
a (a) When a listener moves towards a stationary source apparent frequency
$n' = \left( {\frac{{v + {v_0}}}{v}} \right)\,$$n = 200$…..$(i)$
When listener moves away from the same source
$n'' = \frac{{(v - {v_O})}}{v}n = 160$…..$(ii)$
From $(i)$ and $(ii)$
$\frac{{v + {v_O}}}{{v - {v_O}}} = \frac{{200}}{{160}}$
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