Physics - Wave on String Question with Solution | TestHub

The speed of a transverse wave on a string is given by $v=\sqrt{\frac{T}{\mu }}$

where $T$ is the tension and $\mu$ is the linear mass density.

From the formula, $v\propto \sqrt{T}$, which implies $T\propto v^2$.

Let the initial speed be $v_1$ and the initial tension be $T_1$.

The new speed is increased by $20\%$, so $v_2=v_1+0.20v_1=1.2v_1$.

The new tension $T_2$ is given by:

$\frac{T_2}{T_1}={\left(\frac{v_2}{v_1}\right)}^2=(1.2{)}^2=1.44$

The percentage increase in tension is:

$\frac{T_2-T_1}{T_1}\times 100\%=(1.44-1)\times 100\%=44\%$

Answer: $44\%$