Question

Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously with tensions ' \(\mathrm{T}_1\) ' and ' \(\mathrm{T}_2\) ' respectively. On changing the tension slightly in one of them, the beat frequency remains unchanged. This will happen when (Given \(\rightarrow \mathrm{T}_1>\mathrm{T}_2\) )

• A. \(\mathrm{T}_{1}\) is increased or \(\mathrm{T}_{2}\) is decreased
• B. \(\mathrm{T}_{1}\) is increased by 144
• C. \(\mathrm{T}_{2}\) is decreased by 144
• D. \(T_{1}\) is decreased or \(T_{2}\) is increased

Hint:

The frequency of a wire varies as the square root of its tension, and the beat frequency is the difference of the two frequencies.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For a stretched wire \(f\propto\sqrt{T}\). Since \(T_1>T_2\), \(f_1>f_2\) and the beat frequency is \(f_1-f_2=6\ \text{Hz}\).

Step 2: Effect of changing the tensions
Increasing \(T_1\) or decreasing \(T_2\) pushes the two frequencies further apart and the beat frequency rises.\nDecreasing \(T_1\) or increasing \(T_2\) brings the two frequencies closer.

Step 3: Choose the option
The numerical changes of 144 are not meaningful for a slight change in tension.\nThe option that lowers \(T_1\) or raises \(T_2\) is the one selected.

Final Answer:
Tension \(T_1\) is decreased or \(T_2\) is increased. \[ \boxed{\text{(D) }\text{T}_{1}\text{ is decreased or T}_{2}\text{ is increased}} \]