To stand or to travel

The velocity of a transverse wave on an infinitely long string is $c$. At $t = 0$ the string is flat (i.e., $y(x,t=0) \equiv 0$) and has velocity distribution $v_y(x,t=0) = V_{\scriptscriptstyle 0}\sin\left(kx + \frac{2\pi}{3}\right)$ where $V_{\scriptscriptstyle 0}$ and $k$ are constants.
Hint: See LN ``Wave Phenomena I,'' Sec. 5.1.

(a)

Find the particular solution $y(x,t)$ to the wave equation for the string consistent with the above initial conditions.

(b)

Does the solution found in (a) represent a traveling wave, a standing wave, or neither? If a traveling wave, in what direction is it moving? If a standing wave, re-write your solution for part (a) in the standing wave form $y(x,t) = A(x)\sin(\omega t)$ and find explicitly the function $A(x)$ in terms of no other quantities than $V_{\scriptscriptstyle 0}$, $c$, and $k$.