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NEETPhysicsWaves and Sound

An organ pipe filled with monatomic Neon gas (molar mass = 20 g/mol ) at 27^ C resonates at its fundamental frequency. The pipe is then completely emptied and filled with monatomic Argon gas (molar mass = 40 g/mol ). At what temperature must the Argon gas be maintained so that the pipe resonates at the exact same fundamental frequency?

Options

  1. A54^ C
  2. B-123^ C
  3. C327^ C
  4. D600^ C

Correct answer

C. 327^ C

Step-by-step solution

The fundamental frequency of an organ pipe is directly proportional to the speed of sound in the gas inside it. Since the frequency and the pipe length remain constant, the speed of sound must be the same in both cases. The speed of sound in a gas is given by v = RT M . Since both Neon and Argon are monatomic gases, their ratio of specific heats is the same. Therefore, for the speed of sound to be equal: T₁ M₁ = T₂ M₂ The initial temperature of Neon is T₁ = 27^ C + 273 = 300 ~K . Substituting the given values: 300

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