The linear mass density of a non-uniform wire under constant tension decreases gradually along the wire so that an incident wave is transmitted without reflection. The wire is uniform with mass density  ${\mu }_1$  for $-\infty <x\le 0$  . In this region, a transverse wave has the form  $y(x,t)=0.003\cos (25x-50t)$  where $y\text{ and }x$  are in meters and  t is in seconds. From $x=0\text{ to }x=20m$   the linear mass density decreases gradually from ${\mu }_1\text{ to }\frac{{\mu }_1}{4}$  . For  $20<x\le \infty$ , the linear mass density is $\mu =\frac{{\mu }_1}{4}$  .