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COMEDK2023PhysicsWaves and Sound

A string vibrates with a frequency of 200 ~Hz . When its length is doubled and tension is altered, it begins to vibrate with a frequency of 300 ~Hz . The ratio of the new tension to the original tension is

Options

  1. A9 : 1
  2. B1 : 9
  3. C3 : 1
  4. D1 : 3

Correct answer

A. 9 : 1

Step-by-step solution

Given, aligned & v₁=200 ~Hz , v₂=300 ~Hz , & l₁=l and l₂=2 l & v = 1 2 l T m v T l T v l & T₂ T₁ = [ v₂ v₁ ]^2 [ l₂ l₁ ]^2= [ 300 200 ]^2 [ 2 l l ]^2= 9 1 aligned

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