Question

When tension \( T \) is applied to a sonometer wire of length \( \ell \), it vibrates with the fundamental frequency \( n \). Keeping the experimental setup same, when the tension is increased by 8 newton, the fundamental frequency becomes three times the earlier fundamental frequency (\( n \)). The initial tension applied to the wire in newton was

• A. 2.0
• B. 0.5
• C. 1.0
• D. 2.5

Hint:

The frequency of a vibrating wire is proportional to the square root of the applied tension. Use this relationship to solve for tension changes.

Answer 1

The Correct Option is C

Step 1: Relationship between frequency and tension.
The frequency of a vibrating sonometer wire is related to the square root of the tension \( T \): \[ n \propto \sqrt{T} \] When the tension is increased by 8 newton, the frequency becomes three times the earlier frequency. Therefore, we have: \[ 3n = n \sqrt{\frac{T + 8}{T}} \] This simplifies to: \[ 9 = \frac{T + 8}{T} \] Solving for \( T \): \[ 9T = T + 8 \implies 8T = 8 \implies T = 1 \, \text{newton} \]
Step 2: Conclusion.
The initial tension applied to the wire was 1.0 newton, so the correct answer is (C).