Question

The velocity of a transverse wave is 100 m/sec if the length of the wire I'd doubled and tension in the string I'd doubled then find the final velocity of the wave

Answer 1

The velocity of a transverse wave in a wire under tension T and of linear density $\mu$ is given by: $v = \sqrt{\frac{T}{\mu}}$

On doubling the length, $\mu$ is halved, since mass is constant (and $\mu = \frac{m}{l}$), so the net effect is:

$v' = \sqrt{\frac{4T}{\mu}} = 2v$

So, the final velocity is twice of the initial = 200m/s.

Note: the answer was edited. Sorry for the initial error.