A closed organ pipe of length L and an open organ pipe contain gases of densities \[{{\rho }_{1}}\] and \[{{\rho }_{2}}\] respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open organ pipe is [IIT-JEE (Screening) 2004]

• A.            \[\frac{L}{3}\]                      
• B.            \[\frac{4L}{3}\]
• C.            \[\frac{4L}{3}\sqrt{\frac{{{\rho }_{1}}}{{{\rho }_{2}}}}\]      
• D.            \[\frac{4L}{3}\sqrt{\frac{{{\rho }_{2}}}{{{\rho }_{1}}}}\]