a
(a) In first overtone of organ pipe open at one end,
end, ${n_c} = \frac{{3v}}{{4{l_c}}}$.....$(i)$
Third harmonic or second overtone of organ pipe open at both end,
${n_0} = \frac{{3v}}{{2{l_0}}}$.....$(ii)$
given ${n_c} = {n_o}$
$ \Rightarrow \,\,\,\,\frac{{3v}}{{4{l_c}}} = \frac{{3{v_0}}}{{2{l_0}}}\,\,\,$
$\Rightarrow \,\,\frac{{{l_c}}}{{{l_o}}} = \frac{1}{2}.$