Question

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe $L$ metres 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 $2L$

For first overtone of a closed organ pipe,


$n=3$
$\Rightarrow f=\frac{3v}{4L_{closed}}$

For second overtone of an open organ pipe,


$n=3$
$f^{\prime }=\frac{3v}{2L_{open}}$

According to the question, $f=f^{\prime }$
$\frac{3v}{4L_{closed}}=\frac{3v}{2L_{open}}$

$\Rightarrow L_{open}=2L_{closed}=2L$