Answer
The maximum transverse speed for any point is $~~188~cm/s$
Work Step by Step
$y(x,t) = 15.0~sin(5\pi x/8 - 4 \pi t)$
We can take the derivative to find an equation for the transverse velocity:
$u = (15.0)(-4\pi)~cos(5\pi x/8 - 4 \pi t)$
$u = (-60\pi)~cos(5\pi x/8 - 4 \pi t)$
We can find the maximum transverse speed for any point:
$u = (-60\pi)~cos(5\pi x/8 - 4 \pi t)$
$u = (-60\pi)~(-1)$
$u = 188~cm/s$
The maximum transverse speed for any point is $~~188~cm/s$
