Two open organ pipes of fundamental frequencies \(\mathrm{n}_{1}\) and \(\mathrm{n}_{2}\) are joined in series. The fundamental frequency of the new pipe is

\(\mathfrak{n}=\frac{\mathrm{V}}{2 \ell_{1}} \quad \therefore \quad \ell_{1}=\frac{\mathrm{V}}{2 \mathrm{n}_{1}}\)
\(\mathfrak{n}_{2}=\frac{\mathrm{V}}{2 \ell_{2}} \quad \therefore \quad \ell_{2}=\frac{\mathrm{V}}{2 \mathrm{n}_{2}}\)
\(\mathfrak{n}=\frac{\mathrm{V}}{2 \ell} \quad \therefore \quad \ell=\frac{\mathrm{V}}{2 \mathrm{n}}\)
\(\ell=\ell_{1}+\ell_{2}\)
\(\frac{\mathrm{V}}{2 \mathrm{n}}=\frac{\mathrm{V}}{2 \mathrm{n}_{1}}+\frac{\mathrm{V}}{2 \mathrm{n}_{2}}\)
\(\therefore \frac{1}{\mathrm{n}}=\frac{1}{\mathrm{n}_{1}}+\frac{1}{\mathrm{n}_{2}}\)
\(\therefore \mathrm{n}=\frac{\mathrm{n}_{1} \mathrm{n}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}\)