Two sources of sound $S_1$ and $S_2$ produce sound waves of same frequency $660\, Hz$. A listener is moving from source $S_1$ towards $S_2$ with a constant speed $u\, m/s$ and he hears $10\, beats/s$. The velocity of sound is $330\, m/s$. Then, $u$ equals ... $m/s$
JEE MAIN 2019, Diffcult
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$f=660\,Hz,$ $v=330\,m/s$
$f_{1}=f\left(\frac{v-u}{v}\right) ; \quad f_{2}=f\left(\frac{v+u}{v}\right)$
$\mathrm{f}_{2}-\mathrm{f}_{1}=\frac{\mathrm{f}}{\mathrm{v}}[\mathrm{v}+\mathrm{u}-(\mathrm{v}-\mathrm{u})]$
$10=\mathrm{f}_{2}-\mathrm{f}_{1}=\frac{\mathrm{f}}{\mathrm{v}}[2 \mathrm{u}]$
$u=2.5 \mathrm{m} / \mathrm{s}$
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