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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Frequency of fundamental mode of vibrations of $1^{st}$ closed organ pipe,
From question, $v_{1} - v_{2} = \frac{16}{20}$ $\Rightarrow \frac{v}{4 \times 100} - \frac{v}{4 \times 101} = \frac{16}{20} \Rightarrow \frac{v}{4} \cdot [\frac{1}{100} - \frac{1}{101}] = \frac{16}{20} \Rightarrow \frac{v}{4} [\frac{101 - 100}{101 \times 100}] = \frac{16}{20} \Rightarrow \frac{v}{4} \times \frac{1}{101 \times 100} = \frac{16}{20} \Rightarrow v = \frac{16 \times 101 \times 4 \times 100}{20} = 32320 cm / s . = 323.2 m / s .$

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