QJEEM25Ph27b7: JEE Main 2025 Physics - Class 11 JEEM25Ph27b7 Solution: A closed organ and an open organ tube are filled by two…

$\begin{aligned}& 9^{\text {th }} \text { harmonic of closed pipe }=\frac{9 \mathrm{~V}_1}{4 \ell_1} \\& 4^{\text {th }} \text { harmonic of open pipe }=\frac{2 \mathrm{~V}_2}{\ell_2} \\& \therefore \frac{9 \mathrm{~V}_1}{4 \ell_1}=\frac{2 \mathrm{~V}_2}{\ell_2} \\& \therefore \frac{9}{4 \ell_1} \sqrt{\frac{\mathrm{~B}}{\rho_1}}=\frac{2}{\ell_2} \sqrt{\frac{\mathrm{~B}}{\rho_2} \Rightarrow \frac{\ell_2}{\ell_1}=\frac{8}{9} \sqrt{\frac{\rho_1}{\rho_2}}} \\& \ell_2=\ell_1 \times \frac{8}{9} \times \frac{1}{4}=\frac{20}{9} \mathrm{~cm}\end{aligned}$