Waves on a String: A string of mass $m$ is under tension, and the speed of a wave in the string is $v.$ What will be the speed of a wave in the string if the mass of the string is increased to $2m$ but with no change in the length or tension?

$\frac{v}{2}$

$\frac{v}{\sqrt[\phantom{2}]{2}}$

$v\sqrt[\phantom{2}]{2}$

$2v$

$4v$