Two closed organ pipes of length $100\,cm$ and $101\,cm$ long give $16$ beats in $20\,sec$ when each pipe is sounded in fundamental mode. Calculate velocity of sound .... $ms^{-1}$
Medium
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$\frac{v}{4^{2}}-\frac{v}{4(1+1)}=\frac{16}{20}$
$\Rightarrow \frac{v}{4}\left[\frac{100}{100}-\frac{100}{101}\right]=\frac{4}{5}$
$\Rightarrow v\left[1-\frac{100}{101}\right]=\frac{16}{5}$
$\Rightarrow \frac{v \times 1}{101}=\frac{16}{5}$
$\therefore v=\frac{16 \times 101}{5}=323.2 \mathrm{m} / \mathrm{s}$
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