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Two open end organ pipes of lengths 50 cm and 50.5 cm produce 3 beats/s. Then velocity of sound in air is (The air columns are oscillating in fundamental mode)

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303 m/s

300 m/s

320 m/s

312 m/s

answer is D.

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Detailed Solution

$\begin{array}{l} f_{1} = \frac{V}{2 l_{1}} and f_{2} = \frac{V}{2 l_{2}} \\ ∴ f_{1} - f_{2} = \frac{V}{2} (\frac{1}{50} - \frac{1}{50.5}) \\ \Rightarrow 3 = \frac{V}{2} (\frac{0.5}{50 \times 50.5}) \Rightarrow V = 303 m / s \end{array}$

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