Question

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be

• A. 4L
• B. L
• C. 2L
• D. $\frac{L}{2}$

Answer 1

The correct option is C 2L

Frequency of second overtone of open organ pipe=$\frac{3v}{2l}$

First overtone of closed pipe=$\frac{3v}{4L}$

Hence $\frac{3v}{2l}=\frac{3v}{4L}$

$⟹L=\frac{l}{2}$

$⟹l=2L$