A closed pipe of length / and an open pipe contain gases of densities ${\rho }_1$ and ${\rho }_2$ respectively. The compressibilities are equal in both the pipes. Both the pipes are vibrating in their first overtone with the same frequency. The length of the open organ pipe is

• A

  $\mathrm{l}/3$

• B

  $4\mathrm{l}/3$

• C

  $\frac{4\mathrm{l}}{3}\sqrt{\left(\frac{{\mathrm{\rho }}_1}{{\mathrm{\rho }}_2}\right)}$

• D

  $\frac{4\mathrm{l}}{3}\sqrt{\left(\frac{{\mathrm{\rho }}_2}{{\mathrm{\rho }}_1}\right)}$