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

Answer 1

The correct option is B $2L$

Let $l_0$ be length of open organ pipe,

second overtone of an open organ pipe $=\frac{3v}{2l_0}$
first overtone of a closed pipe of length$L$ is $=\frac{3v}{4L}$

Given
$\frac{3v}{2l_0}=\frac{3v}{4L}$
$2l_0=4L$
$l_0=2L$