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(B) The velocity of a transverse wave in a stretched string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear ma

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$2$

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(B) The velocity of a transverse wave in a stretched string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.Linear mass density $\mu = \rho A = \rho (\pi R^2)$,where $\rho$ is the density of the material and $R$ is the radius of the cross section.Since both strings are made of the same material,$\rho$ is constant. Given that the tension $T$ is the same for both strings,we have $v \propto \frac{1}{\sqrt{R^2}} \propto \frac{1}{R}$.Therefore,$\frac{v_2}{v_1} = \frac{R_1}{R_2}$.Given $R_1 = R$ and $R_2 = R/2$,we get $\frac{v_2}{v_1} = \frac{R}{R/2} = 2$.

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