Two sources of sound A and B are moving towards and away from a...

Given, frequency of sound produced by sources $A$~and $B$,~${f}_{A} = {f}_{B} = 400Hz$

Speed of sound in air, $v = 340ms^{- 1}$

Apparent frequency heard by the observer when source $A$ is moving towards him,

${f}_A^{'} = \dfrac{v}{v - {v}_{S}} \times {f}_{A} = \dfrac{340}{340 - {v}_{S}} \times 400$

Apparent frequency heard by the observer when source $B$ is moving away from him,

${f}_B^{'} = \dfrac{v}{v + {v}_{s}} \times {f}_{B} = \dfrac{340}{340 + {v}_{s}} \times 400$

Given, Beats~$= {f}_A^{'} - {f}_B^{'} = 4$

$\dfrac{340}{340 - {v}_{s}} \times 400 - \dfrac{340}{340 + {v}_{s}} \times 400 = 4$

$⇒ \dfrac{34000 \times 2{v}_{S}}{{340}^{2} - {v}_S^{2}} = 1$

$\dfrac{34000 \times 2{v}_{S}}{3402} = 1$~ & \left[∵ {v}_S^{2} < < {340}^{2}\right]$</p><p>$⇒ {v}_{s} = 1 . 7ms^{- 1}$