JEE Mains · Physics · STD 11 - 14. waves and sound
A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities \(\rho_1\) and \(\rho_{2^{\prime}}\), respectively. The frequency of \(9^{\text {th }}\) harmonic of closed tube is identical with \(4^{\text {th }}\) harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is \(\rho_1: \rho_2=1: 16\), then the length of the open tube is :
- A \(\frac{15}{7} \mathrm{~cm}\)
- B \(\frac{20}{7} \mathrm{~cm}\)
- C \(\frac{15}{9} \mathrm{~cm}\)
- D \(\frac{20}{9} \mathrm{~cm}\)
Answer & Solution
Correct Answer
(D) \(\frac{20}{9} \mathrm{~cm}\)
Step-by-step Solution
Detailed explanation
\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} \\ &…
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