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A closed organ pipe of length \( L \) and an open organ pipe contain gases of densities \( \rho_{1} \) and \( \rho_{2} \) respectively. The
\( \mathrm{P} \) compressibility of gases is equal in both the pipes. Both the

W 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) \( \frac{4 L}{3} \)
(c) \( \frac{4 L}{3} \sqrt{\frac{\rho_{1}}{\rho_{2}}} \)
(d) \( \frac{4 L}{3} \sqrt{\frac{\rho_{2}}{\rho_{1}}} \)
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