wave 
(wāv)
(wāv)v. waved, wav·ing, waves
v.intr.
1. To move freely back and forth or up and down in the air, as branches in the wind.
2. To make a signal with an up-and-down or back-and-forth movement of the hand or an object held in the hand: waved as she drove by.
3. To have an undulating or wavy form; curve or curl: Her hair waves naturally.
v.tr.
1. To cause to move back and forth or up and down, either once or repeatedly: She waved a fan before her face.
2.
a. To move or swing as in giving a signal: He waved his hand. See Synonyms at flourish.
b. To signal or express by waving the hand or an object held in the hand: We waved goodbye.
c. To signal (a person) by using the hand to move in a specified direction: The police officer waved the motorist into the right lane.
3. To arrange into curves, curls, or undulations: wave one's hair.
n.
Phrasal Verb: 1.
a. A ridge or swell moving through or along the surface of a large body of water.
b. A small ridge or swell moving across the interface of two fluids and dependent on surface tension.
2. often waves The sea: vanished beneath the waves.
3. Something that suggests the form and motion of a wave in the sea, especially:
a. A moving curve or succession of curves in or on a surface; an undulation: waves of wheat in the wind.
b. A curve or succession of curves, as in the hair.
c. A curved shape, outline, or pattern.
4. A movement up and down or back and forth: a wave of the hand.
5.
a. A surge or rush, as of sensation: a wave of nausea; a wave of indignation.
b. A sudden great rise, as in activity or intensity: a wave of panic selling on the stock market.
c. A rising trend that involves large numbers of individuals: a wave of conservatism.
d. One of a succession of mass movements: the first wave of settlers.
e. A maneuver in which fans at a sports event simulate an ocean wave by rising quickly in sequence with arms upraised and then quickly sitting down again in a continuous rolling motion.
6. A widespread, persistent meteorological condition, especially of temperature: a heat wave.
7. Physics
a. A disturbance that travels through a medium. Energy is transferred by a wave from one region of the medium to another without causing any permanent displacement of the medium.
b. A graphic representation of the variation of such a disturbance with time.
c. A single cycle of a periodic wave.
wave off
1. To dismiss or refuse by waving the hand or arm: waved off his invitation to join the group.
2. Sports To cancel or nullify by waving the arms, usually from a crossed position: waved off the goal because time had run out.
[Middle English waven, from Old English wafian; see webh- in the Appendix of Indo-European roots.]
waver n.