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MHT CET Medical202623 April 2026Morning ShiftPhysicsWaves and SoundActual

A sonometer wire vibrating in two loops is in resonance with a tuning fork. If tension applied to the string is increased to 16 times the original tension and length of the wire is doubled. It can still be in resonance with the tuning fork provided it vibrates in

Options

  1. Aone loop
  2. Btwo loops
  3. Cthree loops
  4. Dfour loops

Correct answer

A. one loop

Step-by-step solution

The frequency of a vibrating string is given by f = p 2L T , where p is the number of loops, L is the length, T is the tension, and is the linear mass density. Let the initial frequency be f₁ . Given p₁ = 2 , we have: f₁ = 2 2L₁ T₁ For the final state, the tension is increased to 16 times the original tension ( T₂ = 16T₁ ) and the length is doubled ( L₂ = 2L₁ ). The frequency f₂ must be equal to f₁ for the wire to remain in resonance with the same tuning fork. f₂ = p₂ 2L₂ T₂ Equating f₁ and f₂ : 2 2L₁ T₁ = p₂ 2(2L₁

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