Transverse waves of same frequency are generated in two steel wires $A$ and $B$. The diameter of $A$ is twice of $B$ and the tension in $A$ is half that in $B$. The ratio of velocities of wave in $A$ and $B$ is
Medium
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(b) $v = \sqrt {\frac{T}{m}} = \sqrt {\frac{T}{{\pi {r^2}\rho }}} $
$v \propto \frac{{\sqrt T }}{r} $
$\Rightarrow \frac{{{v_A}}}{{{v_B}}} = \sqrt {\frac{{{T_A}}}{{{T_B}}}} .\frac{{{r_B}}}{{{r_A}}} = \sqrt {\frac{1}{2}} .\frac{1}{2} = \frac{1}{{2\sqrt 2 }}$
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