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 - 1 .

Question

TestHub · Accepted Answer

The formula to calculate the fundamental frequency in a closed pipe is given by

$f_{c} = \frac{v}{4 l_{1}} . . . (1)$

And, that in an open pipe is given by

$f_{o} = \frac{v}{2 l_{2}} . . . (2)$

Given that

$|f_{c} - f_{o}| = 7 . . . (3)$

From equations (1), (2) and (3), it follows that

$\frac{v}{4 \times 150} - \frac{v}{2 \times 350} = 7 \Rightarrow \frac{v}{600 cm} - \frac{v}{700 cm} = 7 \Rightarrow \frac{v}{6 m} - \frac{v}{7 m} = 7 \Rightarrow v (\frac{1}{42}) = 7 \Rightarrow v = 42 \times 7 = 294 m s^{- 1}$

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