Explanation:
Frequency of pth overtone of open organ
pipe \( = (p + 1)\frac{v}{{2L}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\)
Where, \(L = \) length of organ pipe and that of closed organ pipe is
\( = (2p + 1)\frac{v}{{4L}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 2 \right)\)
So, the ratio of pth overtone of open to closed
\( = \frac{{(p + 1)\frac{v}{{4L}}}}{{(2p + 1)\frac{v}{{4L}}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{\text{using}}\,{\text{eq}}{\text{.}}\left( {\text{1}} \right)\,{\text{and}}\,\left( {\text{2}} \right)} \right)\)
\( = \frac{{2(p + 1)}}{{(2p + 1)}}\)