Two similar open organ pipe of length $50\, cm$ and $50.5\, cm$ produce $3$ beats per second when sounded together. The velocity of sound in air is ........ $m/s$
Medium
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$L_{1}=50 \mathrm{cm}, L_{2}=50.5 \mathrm{cm}$
as $L_{2}>L_{1},$ so $n_{2}$
For open pipe,
$n=\frac{v}{2 L}$
$n_{1}-n_{2}=3$ beats $/ \mathrm{s}$
$\frac{v}{2}\left(\frac{1}{L_{1}}-\frac{1}{L_{2}}\right)=3$
$\frac{v}{10^{-2}}\left(\frac{1}{50}-\frac{1}{50.5}\right)=6$
$v=\frac{6 \times 50 \times 50.5 \times 10^{-2}}{0.5}=303 \mathrm{m} / \mathrm{s}$
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