Equation 9.36 describes the most general linearly polarized wave on a string. Linear (or ``plane'') polarization (so called because the displacement is parallel to a fixed vector n^) results from the combination of horizontally and vertically polarized waves of the same phase (Eq. 9.39). If the two components are of equal amplitude, but out of phase by 90∘ (say, δv=0, δh=90∘), the result is a circularly polarized wave. In that case:
(a) At a fixed point z, show that the string moves in a circle about the z axis. Does it go clockwise or counterclockwise, as you look down the axis toward the origin? How would you construct a wave circling the other way? (In optics, the clockwise case is called right circular polarization, and the counterclockwise, left circular polarization.)
(b) Sketch the string at time t=0.
(c) How would you shake the string in order to produce a circularly polarized wave?