Wave

A wave is a spatially organized disturbance whose evolution can transmit a pattern and energy through space. Shake one end of a stretched mechanical string: the displacement travels along it while each small piece mainly moves up and down. In a small-amplitude acoustic wave, nearby fluid elements similarly oscillate about their mean positions while the pressure disturbance travels onward. Transport of a wave therefore need not mean bulk transport of the material carrying it.

For a one-dimensional nondispersive travelling wave, $u(x,t)=f(x-ct)$ keeps its shape while moving at wave speed $c$. A sinusoidal example has wavelength $\lambda$ and frequency $f=c/\lambda$. Oppositely travelling disturbances can instead form a standing wave. Interference follows from the superposition principle when the governing equations are linear; nonlinear waves can change shape and interact more strongly. Measuring arrival time, frequency and wave amplitude makes waves useful probes of both a source and the medium between source and receiver.