Physics - Wave on String Question with Solution | TestHub

The speed of a transverse wave on a string is given by $v=\sqrt{\frac{T}{\mu }}$. Initially, let the speed be $v_1=\sqrt{\frac{T_1}{\mu }}$.

The tension is increased by $44\%$, so $T_2=T_1+0.44T_1=1.44T_1$. The linear mass density $\mu$ remains constant as stated in the problem. The new speed $v_2=\sqrt{\frac{T_2}{\mu }}=\sqrt{\frac{1.44T_1}{\mu }}=\sqrt{1.44}\sqrt{\frac{T_1}{\mu }}=1.2v_1$. The percentage change in speed is:$$\frac{v_2-v_1}{v_1}\times 100\%=\frac{1.2v_1-v_1}{v_1}\times 100\%=\frac{0.2v_1}{v_1}\times 100\%=0.2\times 100\%=20\%\text{ increase}$$