Answer
$v_{max} = 9.4~m/s$
Work Step by Step
We can find the speed of the wave as it moves along the string as:
$v = \sqrt{\frac{F_T}{\mu}}$
$v = \sqrt{\frac{50.0~N}{0.00500~kg/m}}$
$v = 100~m/s$
We can find the frequency as:
$f = \frac{v}{\lambda}$
$f = \frac{100~m/s}{2.0~m}$
$f = 50~Hz$
We can find the angular frequency as:
$\omega = 2\pi~f$
$\omega = (2\pi)(50~Hz)$
$\omega = 314~rad/s$
We can find the maximum velocity of a particle on the string as:
$v_{max} = A~\omega$
$v_{max} = (3.0~cm)(314~rad/s)$
$v_{max} = 940~cm/s = 9.4~m/s$
