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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 . . . . "