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(B) The velocity $V$ of a transverse wave travelling on a stretched string is given by the formula $V = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension

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$\frac{1}{2}$

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(B) The velocity $V$ of a transverse wave travelling on a stretched string is given by the formula $V = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.Since $\mu = \rho \cdot A = \rho \cdot \pi r^2$,where $\rho$ is the density of the material and $r$ is the radius of the string,we have $V = \sqrt{\frac{T}{\rho \cdot \pi r^2}}$.Given that the material is the same ($\rho$ is constant) and the tension $T$ is the same,we find that $V \propto \frac{1}{r}$.Therefore,the ratio of the speeds is $\frac{V_A}{V_B} = \frac{r_B}{r_A}$.Given $r_A = 2r_B$,we substitute this into the ratio: $\frac{V_A}{V_B} = \frac{r_B}{2r_B} = \frac{1}{2}$.

Two strings $A$ and $B$ of the same material are stretched by the same tension. The radius of string $A$ is double the radius of string $B$. $A$ transverse wave travels on string $A$ with speed $V_A$ and on string $B$ with speed $V_B$. The ratio $\frac{V_A}{V_B}$ is:

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