Question

Two Velocities in a Traveling Wave? Wave motion is characterized by two velocities: the velocity with which the wave moves in the medium (e.g., air or a string) and the velocity of the medium (the air or the string itself).
Consider a transverse wave traveling in a string. The mathematical form of the wave is
y(x,t) = A sin(kx-omega...

Answer 1

For the answer to the question above,
There is nothing in the equations to suggest that the string moves in the x direction so D) v_x(x,t)=0. 

 y(x,t) = A sin(kx-omega t) 
d{y(x,t)}/d{x} = A k cos(kx - omega t)