挥舞 + 着 + Object
挥舞 (huīwǔ) means "to wave" or "to brandish," describing the action of moving something energetically through the air, such as a flag, weapon, or hand. It emphasizes a vigorous, sweeping motion. It typically takes a concrete object as its complement.
球迷们激动地挥舞着旗帜为球队加油。
Qiúmí men jīdòng de huīwǔ zhe qízhì wèi qiúduì jiāyóu.
The fans excitedly waved flags to cheer for the team.
他挥舞着手中的木棍赶走了那条狗。
Tā huīwǔ zhe shǒu zhōng de mùgùn gǎnzǒu le nà tiáo gǒu.
He waved the wooden stick in his hand to drive away the dog.
孩子们挥舞着小手向我们告别。
Háizimen huīwǔ zhe xiǎo shǒu xiàng wǒmen gàobié.
The children waved their little hands to say goodbye to us.