The fundamental frequency of an air column in pipe ' $\mathrm{A}$ ' closed at one end coincides with second…
The fundamental frequency of an air column in pipe ' $\mathrm{A}$ ' closed at one end coincides with second overtone of pipe ' $\mathrm{B}$ ' open at both ends. The ratio of length of pipe ' $\mathrm{A}$ ' to that of pipe ' $\mathrm{B}$ ' is
$3: 8$
$3: 4$
$1: 6$
$2: 3$
Solution
Fundamental frequency of pipe closed at one end
$\mathrm{n}=\frac{\mathrm{v}}{4 \ell}$
Second overtone of pipe open at both the ends
$\begin{aligned}
& \mathrm{n}^{\prime}=\left(\frac{3 \mathrm{v}}{2 \ell^{\prime}}\right) \\
& \mathrm{n}^{\prime}=\mathrm{n} \\
& \therefore \frac{3 \mathrm{v}}{2 \ell^{\prime}}=\frac{\mathrm{v}}{4 \ell} \\
& \therefore \frac{\ell}{\ell^{\prime}}=\frac{1}{6}
\end{aligned}$