The pipe of length $l_1$ , closed at one end is kept in a chamber of gas of density ${\rho }_1$. A second pipe open at both ends is placed in a second chamber of gas density ${\rho }_2$, the compressibility of both gases is equal. Calculate length of the second pipe if frequency of first one in both the cases are equal.

• A

  $\frac{4}{3}{l}_1\sqrt{\frac{{\rho }_2}{{\rho }_1}}$

• B

  $\frac{4}{3}{l}_1\sqrt{\frac{{\rho }_1}{{\rho }_2}}$

• C

  $l_1\sqrt{\frac{{\rho }_2}{{\rho }_1}}$

• D

  $l_1\sqrt{\frac{{\rho }_1}{{\rho }_2}}$