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 $ 8\,cm, $ then the length of closed pipe is

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

Answer 1

Answer: (D)

Third overtone of an open organ pipe $n_{1}=\frac{4 v}{2 l_{1}}$
Second overtone of closed pipe $n_{2}=\frac{5 v}{4 l_{2}}$
As $n_{1}$ and $n_{2}$ are in resonance.
$n_{1}=n_{2}=n$
$\frac{4 v}{2 l_{1}}=\frac{5 v}{4 l_{2}} $
$\frac{4 v}{2 \times 8}=\frac{5 v}{4 l_{2}}$
$\Rightarrow l_{2}=5 \,cm$