A wave described by y(x,t)=Asin(kx-wt) moves down a string. What is the maximum transverse speed an atom of the string can have? What is the displacement of this atom at this time?
y(x,t)=Asin(kx-wt)
Speed
dy/dt = - Aωcos(kx-ωt),
Max. speed
(dy/dt)max =Aω.
cos(kx-ωt) =1 =>
sin(kx-wt)=0 => x=0