PhysicsAn open organ pipe and closed pipe have same length. The ratio of frequencies of their nth over tone is ……….

An open organ pipe and closed pipe have same length. The ratio of frequencies of their nth over tone is ..........

A
$\frac{n + 1}{2 n + 1}$
B
$\frac{2 (n + 1)}{2 n + 1}$
C
$\frac{n}{2 n + 1}$
D
$\frac{n + 1}{2 n}$

Solution:

For open organ pipe nth overtone $n_{0} = \frac{(n + 1) v}{2 l_{0}}$
For closed organ pipe nth overtone $n_{c} = \frac{(2 n + 1) v}{4 l_{c}}$
$\frac{n_{0}}{n_{c}} = \frac{\frac{n + 1}{2}}{\frac{2 n + 1}{4}} = \frac{2 (n + 1)}{2 n + 1} (∵ l_{0} = l_{c})$