A pipe of length $1.5\ m$ closed at one end is filled with gas and resonates in its fundamental mode with a tuning fork. Another open organ pipe of same dimensions filled with air resonates in its fundamental mode with same tuning fork. If experiment is performed at $30\,^oC$ (speed of sound in air is $360\ m/sec$ at $30\,^oC$), the speed of sound at $0\,^oC$ in gas is ...... $m/sec$ (Neglect end correction)
Diffcult
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For open pipe ${n_0} = \frac{v}{{2l}} = \frac{{360}}{{2 \times 15}} = 120\,{\rm{Hz}}$
Let velocity of sound in gas at $30^{\circ} \mathrm{C}=\mathrm{v}^{\prime}$
${n_1} = \frac{{{v^\prime }}}{{4l}} = \frac{{{v^\prime }}}{{4 \times 1.5}} = \frac{{{v^\prime }}}{6}$
$\mathrm{n}_{1}=\mathrm{n}_{0} \Rightarrow \mathrm{v}^{\prime}=720 \mathrm{\,m} / \mathrm{sec}$
Also $\mathrm{v} \propto \sqrt{\mathrm{T}} \Rightarrow \mathrm{v}=720 \times \sqrt{\frac{273}{303}}=683 \mathrm{\,m} / \mathrm{sec}$
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