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A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities ₁ and _ 2^ , respectively. The frequency of 9^ th harmonic of closed tube is identical with 4^ th harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is ₁: ₂=1: 16 , then the length of the open tube is :

Options

  1. A15 7 ~cm
  2. B20 7 ~cm
  3. C15 9 ~cm
  4. D20 9 ~cm

Correct answer

D. 20 9 ~cm

Step-by-step solution

aligned & 9^ th harmonic of closed pipe = 9 ~V ₁ 4 ₁ & 4^ th harmonic of open pipe = 2 ~V ₂ ₂ & 9 ~V ₁ 4 ₁ = 2 ~V ₂ ₂ & 9 4 ₁ ~B ₁ = 2 ₂ ~B ₂ ₂ ₁ = 8 9 ₁ ₂ & ₂= ₁ 8 9 1 4 = 20 9 ~cm aligned

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