Polarization

We have assumed that the oscillation in the string happen in the y y direction. We could just as easily have had the oscillations happen in the perpendicular direction or a combination. This is referred to as the polarization of the wave. You can consider the motion in the two directions and then add them together (the superposition property lets you do this). So consider two motions that are in phase and have the same wavelength but are perpendicular.

y ( x , t ) = A cos ( k x − ω t ) y ( x , t ) = A cos ( k x − ω t ) z ( x , t ) = A cos ( k x − ω t ) z ( x , t ) = A cos ( k x − ω t ) Lets look at a slice in the y − z y − z plane at position x = 0 x = 0 . Then you get: y ( t ) = A cos ω t y ( t ) = A cos ω t z ( t ) = A cos ω t z ( t ) = A cos ω t or r ⃗ = A cos ω t  ̂ + A cos ω t k ̂ r ⃗ = A cos ω t  ̂ + A cos ω t k ̂ Draw this and show it is a diagonal straight line of movement. The amplitude of the wave is 2 A 2 A

This is an example of a linearly polarized wave. We could have made the motions completely out of phase: y ( x , t ) = A cos ( k x − ω t ) y ( x , t ) = A cos ( k x − ω t ) z ( x , t ) = A sin ( k x − ω t ) z ( x , t ) = A sin ( k x − ω t ) Then at x = 0 x = 0 you get r ⃗ = A cos ω t  ̂ − A sin ω t k ̂ r ⃗ = A cos ω t  ̂ − A sin ω t k ̂ which is a circle. This is an example of a Circularly polarized wave. That is a point on the wave moves in a circular motion in the y − z y − z plane Obviously you can play with the amplitudes and phases of the wave and also get elliptically polarlized waves. Circular and elliptically polarized waves carry angular momentum and well as energy and linear momentum.