A pipe of length ℓ1 , closed at one end is kept in a chamber of gas of density ρ1 . A second pipe open at both ends is placed in a second chamber of gas of density ρ2 . The compressibility of both the gases is equal. Calculate the length of the second pipe if frequency of first overtone in both the cases is equal.
(1) 34ℓ1ρ1ρ2
(2) 34ℓ1ρ2ρ1
(3) ℓ1ρ1ρ2
(4) ℓ1ρ2ρ1