Physics - Wave on String Question with Solution | TestHub

The speed of a transverse wave on a stretched string is given by $v=\sqrt{\frac{T}{\mu }}$, where $T$ is the tension and $\mu$ is the linear mass density.

For the initial state, the tension is $T_1$, so the speed is:

$v_1=\sqrt{\frac{T_1}{\mu }}$

The tension is increased by $T_1$, so the new tension is $T_2=T_1+T_1=2T_1$.

The new speed is:

$v_2=\sqrt{\frac{2T_1}{\mu }}=\sqrt{2}\sqrt{\frac{T_1}{\mu }}=\sqrt{2}{v}_1$

Comparing this with $v_2=x{v}_1$, we get $x=\sqrt{2}$.

Answer: $\sqrt{2}$