Question

Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by $T_1,T_2$ the higher and the lower initial tension in the strings, then it could be said that while making the above changes in tension :

• A. $T_2$ is decreased
• B. $T_2$ is increased
• C. $T_1$ is decreased
• D. $T_1$ is increased

Answer 1

The correct option is C

$T_1$ is decreased

As, $f=\frac{1}{2l}\sqrt{\frac{T}{u}}$

$\therefore f\propto \sqrt{T}$

Given that $T_1>T_2$

$\therefore f_1>f_2$

Initially beat frequency $(f_1-f_2)=6$.

The beat frequency remains unchanged which is possible when $f_2$ increases or $f_1$ decreases. Thus $T_2$ increases or $T_1$ decreases.