A light string with a mass per unit length of $6\mathrm{.}80$ g$/$m has its ends tied to two walls separated by a distance equal to three$-$fourths the length of the string. An object of mass m is suspended from the center of the string, putting a tension in the string.

$($a$)$ Find an expression for the transverse wave speed in the string as a function of the mass of the hanging object. $($Answer in terms of the mass m and note that this is the speed due to the mass$/$unit length and tension.$)$

$($b$)$ What should be the mass of the object suspended from the string in order to produce a wave speed of $70\mathrm{.}0$ m$/$s$?$

kg