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Two closed organ pipes of length 100 cm and 101 cm produces 16 beats in 20 sec when each pipe is sounded in its fundamental mode. Calculate the velocity of sound.

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303 m/s

323.2 m/s

300 m/s

332 m/s

answer is C.

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Detailed Solution

$\begin{array}{l} n_{1} - n_{2} = Δn \\ \frac{V}{4 l_{1}} - \frac{V}{4 l_{2}} = \frac{16}{20} = 0.8 \end{array}$

$\frac{V}{4} (\frac{1}{100} - \frac{1}{101}) = 0.8$

$\Rightarrow V = 32320 cm / s = 323.2 m / s$

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