c
Fundamental frequency of an open pipe of length \(L\) is given by \(n =\frac{ v }{2 L }\) \(\Longrightarrow L =\frac{ v }{2 n }\)

So, we get lengths of two open pipes as \(L _{1}=\frac{ v }{2 n _{1}}\) and \(L _{2}=\frac{ v }{2 n _{2}}\) Now the pipes are join in series.

Fundamental frequency of new open pipe of length \(L _{1}+ L _{2},\)

\(n =\frac{ v }{2\left( L _{1}+ L _{2}\right)}\)

\(n =\frac{ v }{2\left(\frac{ v }{2 n _{1}}+\frac{ v }{2 n _{2}}\right)}\)

\(n=\frac{1}{\frac{1}{n_{1}}+\frac{1}{n_{2}}}\)

\(\Rightarrow n =\frac{ n _{1} n _{2}}{ n _{1}+ n _{2}}\)