A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is ________ m/s.

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answer is 294.

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Detailed Solution

$\begin{aligned} f_{c} = \frac{v}{4 ℓ_{1}} f_{o} = \frac{v}{2 ℓ_{2}} \\ | f_{c} - f_{0} | = 7 \\ \frac{v}{4 \times 150} - \frac{v}{2 \times 350} = 7 \\ \frac{v}{600 cm} - \frac{v}{700 cm} = 7 \\ \frac{v}{6 m} - \frac{v}{7 m} = 7 \\ v (\frac{1}{42}) = 7 \\ v = 42 \times 7 \\ = 294 m / s \end{aligned}$

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