Transverse, Longitudinal & Polarized Waves

A wave travels one way; the medium wiggles another. Comparing those two directions sorts waves into kinds, and for some waves the wiggle direction can even be filtered.

Transverse and longitudinal#

Not every wave is one or the other. Disturb the surface of a still lake and the water particles move in circles or ellipses as the wave passes, with components both along and across the direction of travel.

Polarization#

Thread a stretched string through a narrow slit in a card held perpendicular to the string (the string along x, the card in the y–z plane). If the string vibrates along y and the slit is also along y, the string slides freely in the slit and the wave passes. Turn the card through 90° so the slit is along z: the card now blocks the y motion, and the wave can’t get through. At an intermediate angle only part of the wave passes, and what passes vibrates parallel to the slit. (Two chairs with the string through the gap between their backs make a homemade version.)

Waves are classified by how their particles move in the plane perpendicular to travel:

• Linearly (plane) polarized: always along one fixed direction, e.g. y = A sin ω(t − x/v), or z = A sin ω(t − x/v).
• Circularly polarized: each particle moves in a small circle.
• Elliptically polarized: each particle moves in an ellipse.
• Unpolarized: the displacement direction changes at random.