Let fo be the frequency of first overtone of open organ pipe and fc be the frequency of first overtone for a closed organ pipe.
So fo=2vo2Lo and fc=3vc4Lc
From the data given in the question, fo=fc
so, 2vo2Lo=3vc4Lc
⇒√B0ρoLo=34√BcρcLc [∵v=√Bρ;B is Bulk modulus of gas]
It is given that, the compressibility of two gases is same ∴ B0=Bc=B (say)
⇒1√ρoLo=341√ρcLc
Substituting the given data, we get
1√1×Lo=34×1√9×1
⇒Lo=4 m