An air column is of length 17 cm . The ratio of frequencies of $5^{\text {th }}$ overtone if the air column is closed at one end to that open at both ends is (velocity of sound in air $=340 \mathrm{~ms}^{-1}$ )

Key Concepts
For a closed organ pipe, only odd harmonics exist with frequencies $f_n = (2n-1)\frac{v}{4L}$ where $n=1,2,3,\dots$; the $k^\text{th}$ overtone corresponds to $n = k+1$. For an open organ pipe, all harmonics are present with frequencies $f_n = n\frac{v}{2L}$, where the $k^\text{th}$ overtone corresponds to $n = k+1$.

The fifth overtone in a closed pipe gives $n=6$, so $f_\text{closed} = (2\times6-1)\frac{v}{4L} = \frac{11v}{4L}$.

The fifth overtone in an open pipe gives $n=6$, so $f_\text{open} = 6\cdot\frac{v}{2L} = \frac{3v}{L}$.

The ratio is $\frac{f_\text{closed}}{f_\text{open}} = \frac{\frac{11v}{4L}}{\frac{3v}{L}} = \frac{11v}{4L} \cdot \frac{L}{3v} = \frac{11}{12}$, eliminating dependencies on length and velocity.

The answer is $\frac{11}{12}$.