When a particular string on a musical instrument has a length $L$ and tension $F$$,$ the speed of the wave on the string is $v$$.$ What is the speed of the wave on the string if the length is halved and the tension is doubled?$($A$)$ $$\backslash$frac$\{1\}\{2\}$ v$$($B$)$ $$\backslash$frac$\{1\}\{4\}$ v$$$($C$\backslash )\backslash$sqrt$\{2\}$ v$$($D$)$ $$\backslash$frac$\{\backslash$sqrt$\{2\}\}\{2\}$ v$$($E$)$ $v$