JEE MAIN - Physics (2024 - 27th January Evening Shift - No. 21)
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 __________ $$\mathrm{m} / \mathrm{s}$$.
Answer
294
Explanation
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$$\begin{aligned} & \mathrm{f}_{\mathrm{c}}=\frac{\mathrm{v}}{4 \ell_1} \quad \mathrm{f}_{\mathrm{o}}=\frac{\mathrm{v}}{2 \ell_2} \\ & \left|\mathrm{f}_{\mathrm{c}}-\mathrm{f}_0\right|=7 \\ & \frac{\mathrm{v}}{4 \times 150}-\frac{\mathrm{v}}{2 \times 350}=7 \\ & \frac{\mathrm{v}}{600 \mathrm{~cm}}-\frac{\mathrm{v}}{700 \mathrm{~cm}}=7 \\ & \frac{\mathrm{v}}{6 \mathrm{~m}}-\frac{\mathrm{v}}{7 \mathrm{~m}}=7 \\ & \mathrm{v}\left(\frac{1}{42}\right)=7 \\ & \mathrm{v}=42 \times 7 \\ & =294 \mathrm{~m} / \mathrm{s} \end{aligned}$$
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