wave to/at sb
to 和 at 都可接挥手对象，to 更常指朝某人挥手致意。
I waved to my friend across the street.
我隔着马路向朋友挥手。
摆动；挥动；摇动；（使）呈波浪形；使起伏；把（头发）弄成波浪形；起浪；产生波浪；（棒球中）挥棒落空
to move your hand from side to side, especially to greet someone or say goodbye
反复来回移动
To move back and forth repeatedly and somewhat loosely.
产生波浪
To generate a wave.
挥手(通常在肩膀以上)以示问候或告别
To move one's hand back and forth (generally above the shoulders) in greeting or departure.
呈现波浪形或起伏形态
To have an undulating or wavy form.
使表面不平整；使呈现波浪形或起伏形态
To raise into inequalities of surface; to give an undulating form or surface to.
将头发做成波浪状
To style (the hair) so as to produce a wavy texture.
挥棒未击中投球
To swing and miss at a pitch.
使反复来回移动
To cause to move back and forth repeatedly.
一般现在时
She waves at me every morning.
她每天早上都向我挥手。
一般过去时
He waved goodbye to his friends yesterday.
他昨天向朋友们挥手告别。
现在进行时
The flag is waving in the wind.
旗帜在风中飘扬。
规则动词
She waved at her friend across the street.
她向街对面的朋友挥手。
用法提示：waved 是 wave 的过去式，作动词，表示挥手致意。
He waves to the bus driver every morning.
他每天早晨向公交车司机挥手。
用法提示：waves 是 wave 的第三人称单数，作动词，表示习惯性挥手。
They were waving goodbye as the train left.
火车离开时他们挥手告别。
用法提示：waving 是 wave 的现在分词，作动词，表示挥手告别。
to 和 at 都可接挥手对象，to 更常指朝某人挥手致意。
I waved to my friend across the street.
我隔着马路向朋友挥手。
goodbye/hello 作宾语，说明挥手是为了告别或打招呼。
She waved goodbye to her parents at the airport.
她在机场向父母挥手告别。
表示挥动手中的东西时，wave 作及物动词，宾语后可直接跟 around/about 等副词。
She waved a flag around to celebrate.
她四处挥舞一面旗子来庆祝。
此义为不及物用法，描述物体在风等作用下反复摆动。
The tall grass waved in the breeze.
高高的草在微风中摇曳。
多指树枝、植物或身体缓慢而有节奏地左右摆动；比 wave 更强调有规则的晃动，一般不用于表示挥手问候。
指以固定点为中心作弧形摆动，如门、吊灯、手臂；比 wave 更强调弧形轨迹，通常不表示挥手问候。
多用于旗帜、翅膀等扁平物，快速而较用力地上下或来回拍动；比 wave 更急促，常伴随声音。
多用于叶子、蝴蝶、小旗等轻小物体，表示轻快而不规则的小幅摆动；不像 wave 那样有明显来回动作。
较正式或文学化，指像波浪一样平滑连续地上下起伏，如麦浪、丘陵；比 wave 更突出波浪形状。
grammar · medium
易错句子She waved me when she saw me across the street.
正确表达She waved at me when she saw me across the street.
wave 表示“挥手打招呼／告别”时是不及物动词，必须用介词 at 或 to 引出对象：wave at/to somebody。直接说 wave somebody 通常表示“挥手示意某人（做某事）”（如 wave somebody over），所以这里要补上 at。
grammar · medium
易错句子The dog was happy and waved its tail.
正确表达The dog was happy and wagged its tail.
狗摇尾巴英语固定用 wag its tail，wag 专指尾巴等来回摇动；wave 强调像波浪一样的摆动，不能用来描述狗尾巴。把 waved 改成 wagged 即可。
grammar · medium
易错句子He wave at me every morning.
正确表达He waves at me every morning.
主语 He 是第三人称单数，一般现在时的动词要加 -s，所以用 waves；汉语动词没有这种词形变化，学习者容易漏掉 -s。
针对“使呈波浪形；将头发做成波浪状”这一义项，“straighten”指把头发等弄直，是直接反义词；不适用于“挥手、摇动”等义项。
针对“使表面呈波浪形/起伏”这一义项，“flatten”指使表面变平，是直接反义词；不适用于“挥手问候”等义项。
挥手告别
She waved goodbye to her friends at the station.
她在车站向朋友们挥手告别。
挥手问候
He waved hello from across the street.
他在街对面挥手问候。
挥动手
She waved her hand to get the waiter's attention.
她挥了挥手以引起服务员的注意。
向某人挥手
The children waved to their parents as the bus left.
公交车离开时，孩子们向父母挥手。
挥动旗帜
Fans waved flags to support their team.
球迷们挥动旗帜为他们的球队加油。
对…说再见；放弃对…的希望
If you keep spending like this, you can wave goodbye to your savings.
如果你继续这样花钱，你就要和你的积蓄说再见了。
认输；投降
After months of resistance, the company finally waved the white flag and accepted the takeover.
经过数月的抵抗，公司最终举起白旗，接受了收购。
挥动魔杖；轻易解决问题
You can't just wave a magic wand and make all your debts disappear.
你不能只是挥挥魔杖，就让所有债务消失。
在空中挥舞双手，仿佛你根本不在乎。
From the 1993 hip-hop song 'Hip Hop Hooray' by Naughty by Nature. The lyric urges the crowd to raise and wave their hands, and it has become a widely known party chant.
出自1993年Naughty by Nature乐队的嘻哈歌曲《Hip Hop Hooray》。这句歌词号召人群举起并挥舞双手，已成为广为人知的派对口号。
我不是在挥手，我是在溺水。
From the song 'Waving Through a Window' in the Tony Award-winning musical Dear Evan Hansen. The line metaphorically expresses feeling desperate for help while being perceived as casually greeting.
出自托尼奖获奖音乐剧《致埃文·汉森》中的歌曲《Waving Through a Window》。这句歌词以隐喻方式表达了一种渴望帮助却被误认为是在随意打招呼的绝望感受。
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挥白旗（表示投降或认输）
After hours of debate, they finally waved the white flag.
经过数小时的辩论，他们最终挥白旗认输。