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MHT CET20225 Aug 2022Morning ShiftPhysicsWaves and SoundActual

The ratio of the speed of sound in helium gas to that in nitrogen gas at the same temperature is ( _ He = 5 3 , _ N ₂ = 7 5 , M_ He =4, M_ N ₂ =28 )

Options

  1. A5 3
  2. B7 5
  3. C2 7
  4. D5 3

Correct answer

A. 5 3

Step-by-step solution

The correct option is (A). Concept: Newton-Laplace equation for the speed of sound in an ideal gas is given by, c= P where is the speed of sound, is the adiabatic index, P the pressure and the density of the gas. On introducing pressure P= R T M by using the ideal gas equation, the speed of sound can be written as c= R T M . The speed of sound is proportional to the square root of the ratio of adiabatic index y and molecular weight M , i.e., c M . On taking the ratio for Helium and Nitrogen: c_ He c_ N ₂ = _ He M_

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