"move back and forth," Old English wafian "to wave with the hands" (related to wæfre "wavering, restless"), from Proto-Germanic *wab- (cf. Old Norse vafra "to hover about," Middle High German waben "to wave, undulate"), possibly from PIE root *webh- "to move to and fro; to weave" (see weave (v.)). Meaning "to make a sign by a wave of the hand" is from 1510s. Related: Waved; waving.
I was much further out than you thought
And not waving but drowning.
"moving billow of water," 1520s, from wave (v.), replacing Middle English waw, which is from Old English wagian "to move to and fro" (cf. Old Saxon, Old High German wag, Old Frisian weg, Old Norse vagr "water in motion, wave, billow," Gothic wegs "tempest;" see wag (v.)). The usual Old English word for "moving billow of water" was yð.
The "hand motion" meaning is recorded from 1680s; meaning "undulating line" is recorded from 1660s. Of people in masses, first recorded 1852; in physics, from 1832. Sense in heat wave is from 1843. The crowd stunt in stadiums is attested under this name from 1984, the thing itself said to have been done first Oct. 15, 1981, at the Yankees-A's AL championship series game in the Oakland Coliseum; soon picked up and popularized at University of Washington. To make waves "cause trouble" is attested from 1962.
A disturbance traveling through a medium by which energy is transferred from one particle of the medium to another without causing any permanent displacement of the medium itself.
A graphic representation of the variation of such a disturbance with time.
A single cycle that is representative of such a disturbance.
A disturbance, oscillation, or vibration, either of a medium and moving through that medium (such as water and sound waves), or of some quantity with different values at different points in space, moving through space (such as electromagnetic waves or a quantum mechanical wave described by the wave function). See also longitudinal wave, transverse wave, wave function. See Note at refraction.
In physics, any regularly recurring event, such as surf coming in toward a beach, that can be thought of as a disturbance moving through a medium. Waves are characterized by wavelength, frequency, and the speed at which they move. Waves are found in many forms.
Note: The motion of a wave and the motion of the medium on which the wave moves are not the same: ocean waves, for example, move toward the beach, but the water itself merely moves up and down. Sound waves are spread by alternating compression and expansion of air.