The ratio of frequencies of the second overtone produced by an open...

For an open pipe of length $L$, the frequency of the $n$-th harmonic is $f_n = \dfrac{nv}{2L}$.

The second overtone corresponds to the third harmonic ($n = 3$).

$f_{o} = \dfrac{3v}{2L}$

For a closed pipe of length $L$, the frequency of the $m$-th harmonic is $f_m = \dfrac{mv}{4L}$, where $m$ is an odd integer.

The second overtone corresponds to the fifth harmonic ($m = 5$).

$f_{c} = \dfrac{5v}{4L}$

The ratio of their frequencies is:

$\dfrac{f_{o}}{f_{c}} = \dfrac{\dfrac{3v}{2L}}{\dfrac{5v}{4L}} = \dfrac{3}{2} \times \dfrac{4}{5} = \dfrac{6}{5}$

Answer: $6 : 5$