Waves

Traveling Disturbances

A wave is a disturbance that travels through space, carrying energy without transporting matter. A cork bobs on water without drifting forward.

Key quantities include wavelength $\lambda$ (crest-to-crest distance), frequency $f$ (oscillations per second in Hz), and period $T = 1/f$. The fundamental wave relation connects them: $$v = f\lambda$$

Common Pitfall: Never confuse frequency with period. They are reciprocals ($f = 1/T$): high frequency means a short period.

Wave Behaviors

The signature behavior distinguishing waves from particles is superposition and interference: when two waves overlap, their displacements add.

Other hallmarks include diffraction (bending around obstacles) and the Doppler effect (frequency shift from relative motion).

Common Pitfall: Thinking a wave carries matter along with it. The medium oscillates locally while only energy moves onward.