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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 :

  1. A \(\frac{15}{7} \mathrm{~cm}\)
  2. B \(\frac{20}{7} \mathrm{~cm}\)
  3. C \(\frac{15}{9} \mathrm{~cm}\)
  4. D \(\frac{20}{9} \mathrm{~cm}\)
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Answer & Solution

Correct Answer

(D) \(\frac{20}{9} \mathrm{~cm}\)

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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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