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Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String

A sonometer wire carrying a 4 kg load vibrates in its fundamental mode when excited by a tuning fork of frequency 416 Hz . If the length of the wire between the bridges is subsequently doubled, what must the load be changed to in order to maintain the fundamental mode?

Options

  1. A16 kg
  2. B8 kg
  3. C2 kg
  4. D1 kg

Correct answer

A. 16 kg

Step-by-step solution

The fundamental frequency of a sonometer wire is given by f = 1 2L T , where L is the length, T is the tension, and is the linear mass density. The tension T is provided by the load M , so T = Mg . Since the frequency f and linear mass density remain constant, we have M L = constant . Therefore, M₁ L₁ = M₂ L₂ . Given M₁ = 4 kg , L₁ = L , and L₂ = 2L , substituting these values gives: 4 L = M₂ 2L 2 L = M₂ 2L M₂ = 4 M₂ = 16 kg

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