An organ pipe ${P_1}$ closed at one end vibrating in its first overtone and another pipe ${P_2}$ open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of ${P_1}$ and ${P_2}$ is
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(c) First overtone of closed organ pipe ${n_1} = \frac{{3v}}{{4{l_1}}}$
Third overtone of open organ pipe ${n_2} = \frac{{4v}}{{2{L_2}}}$
${n_1} = {n_2}$ (Given)
Third overtone of open organ pipe ${n_2} = \frac{{4v}}{{2{L_2}}}$
${n_1} = {n_2}$ (Given)
$ \Rightarrow $$\frac{{3v}}{{4{L_1}}} = \frac{{4v}}{{2{L_2}}} \Rightarrow $$\frac{{{L_1}}}{{{L_2}}} = \frac{3}{8}$
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