Thank you for reporting, we will resolve it shortly
Q.
The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20\,cm$, the length of the open organ pipe is
For closed organ pipe, third harmonic
$ = \frac{3v}{4l} $
For open organ pipe, fundamental frequency
$= \frac{v}{2l'}$
Given,
$ \frac{3v}{4l} = \frac{v}{2l'} $
$\Rightarrow l' = \frac{4l}{3 \times2} = \frac{2l}{3} $
$= \frac{2 \times20}{3} $
$= 13.33\, cm $