## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

$v_{max} = 9.4~m/s$
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: $v_{max} = A~\omega$ $v_{max} = (3.0~cm)(314~rad/s)$ $v_{max} = 940~cm/s = 9.4~m/s$