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
- A16 kg
- B8 kg
- C2 kg
- 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