The verb 'wave' originates from the Old English wafian, meaning "to wave with the hands, fluctuate." This term is rooted in the Proto-Germanic wab-, conveying a sense of moving to and fro, which itself may derive from the Proto-Indo-European root webh-, meaning "to weave" or "to move quickly." The semantic connection lies in the back-and-forth motion common to weaving, waving, and fluctuating. The addition of the '-ing' suffix, from Old English, transforms the verb into its present participle or gerund form, 'waving,' which describes the ongoing action or state of making such a motion.

Structure: wave (to move loosely) + ing (present participle suffix) wave: From Old English wafian (to wave, fluctuate), of Germanic origin. It functions as the core verb root. ing: From Old English -ende, -unge, a suffix forming present participles and verbal nouns.