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

$f_c=\frac{v}{4l_1} ...\left(1\right)$

And, that in an open pipe is given by

$f_o=\frac{v}{2l_2} ...\left(2\right)$

Given that

$\left|f_c-f_o\right|=7 ...\left(3\right)$

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

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