source: [たまこまーけっとの北白川たまこが商店街で手を振るGIF画像｜無料GIF画像検索 GIFMAGAZINE 935611]

1. no object move one's hand to and fro in greeting or as a signal:

(あいさつ･合図などのために) «…に/…を求めて/…するように» 手を振る «to, at/for/to do»

e.g. he waved to me from the train.

with object move (one's hand or arm, or something held in one's hand) to and fro:

〖～ A at/to B〗 B〈人〉にA〈手･手に持った物など〉を振る; …を振り回す(around, ｟英｠ about)

e.g. he waved a sheaf of papers in the air.

with object convey (a greeting or other message) by moving one's hand or something held in it to and fro:

〖～(A) B/B (to A)〗 (A〈人〉に)手を振ってB〈あいさつなど〉をする

e.g. we waved our farewells

e.g. with two objects : she waved him goodbye.

with object and adverbial of direction instruct (someone) to move in a particular direction by moving one's hand:

〖～ A＋副詞〗 (ある方向へ行くよう)A〈人など〉に手を振って合図, 指示する; (ある方向へ)A〈物〉を手を振って移す; (ある方向を)A〈手など〉を振って指し示す (!〖副詞〗は方向などの表現)

e.g. he waved her back.

2. move to and fro with a swaying or undulating motion while remaining fixed to one point:

〈旗･枝などが〉(ゆらゆらと)揺れる, 揺らめく

e.g. the flag waved in the wind.

3. with object style (hair) so that it curls slightly:

〈髪〉にウェーブ, パーマをかける

e.g. her hair had been carefully waved for the evening.

no object (of hair) grow with a slight curl:

〈髪が〉ウェーブしている

e.g. (as adjective waving) : thick, waving gray hair sprouted back from his forehead.

1. a long body of water curling into an arched form and breaking on the shore.

波

a ridge of water between two depressions in open water:

e.g. gulls and cormorants bobbed on the waves.

a shape seen as comparable to a breaking wave:

(地形の)起伏, うねり

e.g. a wave of treetops stretched to the horizon.

(usually the wave) an effect resembling a moving wave produced by successive sections of the crowd in a stadium standing up, raising their arms, lowering them, and sitting down again.

｟米｠ ; 〖the ～〗 (スポーツ観戦などで観衆が行う)ウェーブ(｟英｠ Mexican wave)

(the waves) literary the sea.

〖the ～s〗 海, 大洋

2. a sudden occurrence of or increase in a specified phenomenon, feeling, or emotion:

〖通例単数形で〗(好ましくない活動･行為などの)急増, 頻発; (感情などの)急激な高まり; (物事･動向などの)波, 傾向 (!しばしばa ～ of ...の形で用い, 通例単数扱い)

e.g. a wave of strikes had effectively paralyzed the government

e.g. horror came over me in waves.

3. a gesture or signal made by moving one's hand to and fro:

〖通例単数形で〗(手･旗などを)振ること; 振って行う合図

e.g. he gave a little wave and walked off.

4. a slightly curling lock of hair:

(髪の)縮れ, ウェーブ(をかけること)

e.g. his hair was drying in unruly waves.

a tendency to curl in a person's hair:

e.g. her hair has a slight natural wave.

5. Physics a periodic disturbance of the particles of a substance which may be propagated without net movement of the particles, such as in the passage of undulating motion, heat, or sound. See also standing wave and traveling wave.

〘物理〙 (音･光などの)波動, 波

a single curve in the course of a wave.

a variation of an electromagnetic field in the propagation of light or other radiation through a medium or vacuum.

make waves informal

create a significant impression:

e.g. he has already made waves as a sculptor.

cause trouble:

e.g. I don't want to risk her welfare by making waves.

dismiss something as unnecessary or irrelevant:

e.g. he waved the objection aside and carried on.

use one's hand to give a signal to stop to a driver or vehicle.

waveless | ˈwāvləs | adjective

wavelike adjective

Old English wafian (verb), from the Germanic base of waver; the noun by alteration (influenced by the verb) of Middle English wawe ‘(sea) wave’.

See usage at waive.