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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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Transverse wave travels faster in thinner wire

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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.Since $\mu = \rho A = \rho (\pi R^2)$,where $\rho$ is the density of the material and $A$ is the cross-sectional area,we have:$v = \sqrt{\frac{T}{\rho \pi R^2}} = \frac{1}{R} \sqrt{\frac{T}{\rho \pi}}$.From this expression,it is clear that $v \propto \frac{1}{R}$.Since $R_{1} > R_{2}$,the velocity $v_{1}$ in the thicker wire will be less than the velocity $v_{2}$ in the thinner wire $(v_{1} Therefore,the transverse wave travels faster in the thinner wire.

Two $Cu$ wires of radii $R_{1}$ and $R_{2}$ are such that $(R_{1} > R_{2})$. Then which of the following is true?

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