A closed organ pipe $150 \mathrm{~cm}$ long gives $7$ beats per second with an open organ pipe of length $350 \mathrm{~cm}$, both vibrating in fundamental mode. The velocity of sound is_________ $\mathrm{m} / \mathrm{s}$.
JEE MAIN 2024, Diffcult
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$ \mathrm{f}_{\mathrm{c}}=\frac{\mathrm{v}}{4 \ell_1} \quad \mathrm{f}_{\mathrm{o}}=\frac{\mathrm{v}}{2 \ell_2} $
$ \left|\mathrm{f}_{\mathrm{c}}-\mathrm{f}_0\right|=7 $
$ \frac{\mathrm{v}}{4 \times 150}-\frac{\mathrm{v}}{2 \times 350}=7 $
$ \frac{\mathrm{v}}{600 \mathrm{~cm}}-\frac{\mathrm{v}}{700 \mathrm{~cm}}=7 $
$ \frac{\mathrm{v}}{6 \mathrm{~m}}-\frac{\mathrm{v}}{7 \mathrm{~m}}=7 $
$ \mathrm{v}\left(\frac{1}{42}\right)=7 $
$ \mathrm{v}=42 \times 7 $
$ =294 \mathrm{~m} / \mathrm{s}$
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