Definition of wave verb from the Oxford Advanced American Dictionary

     

    wave

     verb
    verb
    NAmE//weɪv//
     
    Verb Forms present simple I / you / we / they wave
     
    he / she / it waves
     
    past simple waved
     
    -ing form waving
     
     
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    move hand/arm
  1. 1[intransitive, transitive] to move your hand or arm from side to side in the air in order to attract attention, say hello, etc. The people on the bus waved and we waved back. wave at/to somebody Why did you wave at him? wave something (about/around) A man in the water was shouting and waving his arms around frantically. wave something at somebody She waved her hand dismissively at the housekeeper. wave something to somebody My mother was crying as Iwaved goodbye to her. wave somebody something My mother was crying as Iwaved her goodbye.
  2. 2[intransitive, transitive] to show where something is, show someone where to go, etc. by moving your hand in a particular direction wave + adv./prep. She waved vaguely in the direction of the house. wave something/somebody + adv./prep. “He's over there,” said Ali,waving a hand toward some trees. I showed my pass to the security guard and he waved me through. She waved me away impatiently.
  3. 3[transitive] to hold something in your hand and move it from side to side wave something Crowds lined the route, waving flags and cheering. wave something + adv./prep. “I'm rich!” she exclaimed, waving the money under his nose.
  4. move freely
  5. 4[intransitive] to move freely and gently, for example in the wind, while one end or side is held in position The flag waved in the breeze.
  6. hair
  7. 5[intransitive] to curl slightly His hair waves naturally.
  8. Idioms
    fly/show/wave the flag
     
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    to show your support for your country, an organization, or an idea to encourage or persuade others to do the same
    like waving a red flag in front of a bull
     
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    something that is likely to make someone very angry
    Phrasal Verbswave somethingaside/awaywave something/somebodydownwave somebodyoff
See the Oxford Advanced Learner's Dictionary entry: wave