\begin{problem*}{13.16}
A light string with a mass per unit length of $8.00\U{g/m}$ has its
ends tied to two walls seperated by a distance equal to three-fourths
the length of the string (Figure P13.16).  An object of mass
$m$ is suspended from the center of the string, putting a tension in
the string.  \Part{a} Find an expression for the transverse wave speed
in the string as a function of the mass of the hanging
object.  \Part{b} What should be the mass of the object suspended from
the string so as to produce a wave speed of $60.0\U{m/s}$.
\begin{center}
\begin{asy}
import Mechanics;

real u=1cm;
real L=3u;      // length of string
real D=3L/4;    // wall separation
real dx = 12pt; // length of bonus string for hanging mass & wall above string
real r = 12pt;  // radius of hanging mass

Mass m = Mass(radius=r, L="m");
pair junction = m.center + (0, r+dx);
real theta = asin(D/L) * 180 / pi;
pair wall_join_r = junction + L/2*dir(90-theta);
pair surf_ur = wall_join_r + (0, dx);
pair surf_lr = (surf_ur.x, m.center.y - r - dx);
Surface s_r = Surface(pFrom=surf_lr, pTo=surf_ur);
pair wall_join_l = xscale(-1)*wall_join_r;
pair surf_ul = xscale(-1)*surf_ur;
pair surf_ll = xscale(-1)*surf_lr;
Surface s_l = Surface(pFrom=surf_ul, pTo=surf_ll);
Distance d = Distance(pFrom=wall_join_l, pTo=wall_join_r, L="$3L/4$");

draw(m.center -- junction);
draw(wall_join_l -- junction -- wall_join_r);
s_r.draw();
s_l.draw();
d.draw();
m.draw();
\end{asy}
\end{center}
\end{problem*}

\begin{solution}
\end{solution}
