The $4^{\text {th }}$ overtone of a closed organ pipe is same as that of $3^{\text {rd }}$ overtone of an…
The $4^{\text {th }}$ overtone of a closed organ pipe is same as that of $3^{\text {rd }}$ overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:
$9: 8$
$7: 9$
$8: 9$
$9: 7$
Solution
$4^{\text {th }}$ overtone for closed organ pipe $\rightarrow 9^{\text {th }}$ harmonic $3^{\text {rd }}$ overtone for open organ pipe $\rightarrow 4^{\text {th }}$ harmonic
$\begin{aligned} & 9\left(\frac{V}{4 I_c}\right)=4\left(\frac{V}{2 I_o}\right) \\ & \frac{I_c}{I_o}=\frac{9}{8}\end{aligned}$