Progressive Waves

Progressive wave — a wave that transfers energy from one place to another without transferring matter. The particles of the medium oscillate about fixed positions; they do not travel with the wave.

Example: a float on water bobs up and down as a wave passes but stays roughly where it started. Energy crosses the pond; the water does not.

Displacement — the distance of a point from its equilibrium position, with direction. A vector, so it can be negative.

Amplitude — the maximum displacement from equilibrium. Always positive, and related to the energy the wave carries.

Wavelength (λ) — the distance between two adjacent points in phase, for example crest to crest.

Period (T) — the time for one complete oscillation.

Frequency (f) — the number of complete oscillations per second, measured in hertz. f = 1/T.

Phase — the position of a point within its oscillation cycle, measured as an angle. Two points in phase are at the same point in their cycles, an exact whole number of wavelengths apart. Two points in antiphase are exactly half a cycle apart, so one is at a crest as the other is at a trough.

Phase difference — measured in radians or degrees. A separation of one wavelength corresponds to 2π radians or 360°, half a wavelength to π radians or 180°.

Transverse waves — the oscillations are perpendicular to the direction of energy transfer. Light and all electromagnetic waves, water waves and waves on a string.

Longitudinal waves — the oscillations are parallel to the direction of energy transfer, producing regions of compression and rarefaction. Sound is the standard example.

Why the distinction matters — it is not a piece of terminology for its own sake. Only transverse waves can be polarised, because only they have a plane of oscillation to restrict. That single consequence is why the classification is worth knowing.

Wavefronts — lines joining points that are all in phase, drawn one wavelength apart. They are perpendicular to the direction of travel, which makes them a convenient way to picture reflection, refraction and diffraction.