Two copper wires of radii $r_1$ and $r_2\left(r_1>r_2\right)$ are subjected to the same tension and are…
Two copper wires of radii $r_1$ and $r_2\left(r_1>r_2\right)$ are subjected to the same tension and are plucked. The transverse waves will
not travel through both the wires
travel with the same velocity in both the wires
travel faster in the thinner wire
travel faster in the thicker wire
Solution
The velocity of a transverse wave on string is given by
$v=\sqrt{\frac{T}{\rho A}}$
$v \propto \frac{1}{\sqrt{A}}$
or $v \propto \frac{1}{R}$
or $v \propto \frac{1}{R}$
Therefore, transverse wave travels faster on thinner wire.