c
(c) Frequency of first over tone of closed pipe \(=\) Frequency of first over tone of open pipe 

\( \Rightarrow \frac{{3v}}{{4{L_1}}} = \frac{v}{{{L_2}}}\)

\( \Rightarrow \frac{3}{{4{L_1}}}\sqrt {\frac{{\gamma P}}{{{\rho _1}}}} \)\( = \frac{1}{{{L_2}}}\sqrt {\frac{{\gamma P}}{{{\rho _2}}}} \) 

\(\left[ {\because v = \sqrt {\frac{{\gamma P}}{\rho }} } \right]\) 

\( \Rightarrow {L_2} = \frac{{4{L_1}}}{3}\sqrt {\frac{{{\rho _1}}}{{{\rho _2}}}} = \frac{{4L}}{3}\sqrt {\frac{{{\rho _1}}}{{{\rho _2}}}} \)