wavelength n.

"moving billow of water," 1520s, alteration (by influence of wave (v.)) of Middle English waw, which is from Old English wagian "to move to and fro," from Proto-Germanic *wag- (source also of Old Saxon, Old High German wag, Old Frisian weg, Old Norse vagr "water in motion, wave, billow," Gothic wegs "tempest"), probably from PIE root *wegh- "to go, move." 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.

Old English lengðu "property of being long or extended in one direction; distance along a line," from Proto-Germanic *langitho, abstract noun from *langaz "long" (root of Old English lang; see long (adj.)) + *-itho, abstract noun suffix (see -th (2)). Cognate with Old Norse lengd, Old Frisian lengethe, Dutch lengte.

Figurative sense of "the distance one goes, extremity to which something is carried" is from 1690s. Phrase at length "to full extent" is attested from c. 1500. As "the length of a swimming pool," 1903. From the notion of "a piece or portion of the extent of anything" come the theater slang sense "a 42-line portion of an actor's part" (1736) and the sporting sense "the length of a horse, car, etc. in a race" used as a unit of measure (1650s).