A closed organ pipe 150cm long gives 7 beats per second with an...

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

${f}_{c} = \dfrac{v}{4{l}_{1}} . . . \left(1\right)$

And, that in an open pipe is given by

${f}_{o} = \dfrac{v}{2{l}_{2}} . . . \left(2\right)$

Given that

\left|{f}_{c} - {f}_{o}\right| = 7 . . . \left(3\right)$</p><p>From equations (1), (2) and (3), it follows that</p><p>$\dfrac{v}{4 \times 150} - \dfrac{v}{2 \times 350} = 7 ⇒ \dfrac{v}{600cm} - \dfrac{v}{700cm} = 7 ⇒ \dfrac{v}{6m} - \dfrac{v}{7m} = 7 ⇒ v\left(\dfrac{1}{42}\right) = 7 ⇒ v = 42 \times 7 = 294m{s}^{- 1}$