The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe \( L \) metre long. The length of the open pipe will be

Frequency of 2nd overtone of open pipe \( \frac{3v}{L_o} \) equals 1st overtone of closed pipe \( \frac{3v}{4L_c} \). Therefore, \( L_o = \frac{4}{3} \) wait, 2nd overtone of open pipe is \( \frac{3v}{L_o} \), 1st overtone of closed pipe is \( \frac{3v}{4L} \). So \( \frac{3v}{L_o} = \frac{3v}{4L} \Rightarrow L_o = 4L \).