Physics - Wave on String Question with Solution | TestHub

The frequency of the fundamental mode of a stretched string is given by $f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

This implies $f\propto \sqrt{T}$

Let the initial tension be $T$ and the initial frequency be $f$.

When the tension is increased by $3\text{ kg wt}$, the new tension is $T+3$ and the new frequency is $f^{\prime }$.

Given that the frequency increases in the ratio $2:3$, we have $\frac{f}{f^{\prime }}=\frac{2}{3}$

$\frac{\sqrt{T}}{\sqrt{T+3}}=\frac{2}{3}$

Squaring both sides, we get:

$\frac{T}{T+3}=\frac{4}{9}$

$9T=4T+12$

$5T=12$

$T=2.4\text{ kg wt}$

Answer: $2.4\mathrm{kg}\omega \mathrm{t}$