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 90o (say, δv = 0, δh = 90o), 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?