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Polarization

One nice feature of waves in a taut string is that they explicitly illustrate the phenomenon of polarization: if we change our notation slightly to label the string's equilibrium direction (and therefore the direction of propagation of a wave in the string) as  z,  then there are two orthogonal choices of ``transverse'' direction:  x  or  y. We can set the string ``wiggling'' in either transverse direction, which we call the two orthogonal polarization directions.

Of course, one can choose an infinite number of transverse polarization directions, but these correspond to simple superpositions of x- and y-polarized waves with the same phase.

One can also superimpose x- and y-polarized waves of the same frequency and wavelength but with phases differing by $\pm \pi/2$. This gives left- and right-circularly polarized waves; I will leave the mathematical description of such waves (and the mulling over of its physical meaning) as an ``exercise for the student . . . . ''