Question

The third overtone of an open organ pipe is in resonance with the second overtone of a closed organ pipe. If the length of the open pipe is $8cm,$ then the length of closed pipe is

• A. $10cm$
• B. $8cm$
• C. $12cm$
• D. $5cm$

Answer 1

Answer: (D)

Third overtone of an open organ pipe $n_1=\frac{4v}{2l_1}$
Second overtone of closed pipe $n_2=\frac{5v}{4l_2}$
As $n_1$ and $n_2$ are in resonance.
$n_1=n_2=n$
$\frac{4v}{2l_1}=\frac{5v}{4l_2}$
$\frac{4v}{2\times 8}=\frac{5v}{4l_2}$
$\Rightarrow l_2=5cm$