Particle histories versus snapshots

A transverse wave on a string is described by $y(x,t) = \Re\left\{ \underline{A} e^{i(kx -\omega_o t)}\right\}$, where $\underline{A} = (4 - 3i) \times 10^{-2}$ m, $k = 3.14$ m$^{-1}$, and $\omega_o = 31.4$ s$^{-1}$.

(a)

Sketch a snapshot of the string at $t = 0$ s for the range $0<x<4$ m.
Note: Again, for these sketches you may make a plot with a computer or graphing calculator and then sketch of what you see on your problem set, being sure to write down on your sketch the approximate value of the location and value ($x$ and $y$ values) of the maximum.

(b)

Sketch a second snapshot of the string at $t=0.04$ s. By comparing your two sketches, estimate the speed of the wave, and compare this result with the ratio $\omega/k$.

(c)

Sketch a particle history for the particle at $x = 1$ m, starting at $t = 0$ and going for two periods.