The compound adjective "wave-like" is a transparent modern English formation. Its first element, "wave," originates from the Old English verb wafian, meaning "to wave with the hands, to fluctuate," which itself is rooted in a common Germanic base conveying restless motion. The second element, "-like," is an extremely productive adjectival suffix descended from the Old English noun līc, meaning "body" or "form," which evolved to signify similarity or resemblance. When combined, the literal construction "having the form of a wave" directly and logically yields the modern abstract meaning used to describe any undulating pattern, motion, or shape, from ocean swells to sound vibrations.

Structure: wave (undulating motion) + like (having the characteristics of) wave: From Old English 'wafian' (to wave, fluctuate), of Germanic origin. Functions as the base noun/adjective denoting the core concept. like: From Old English 'līc' (body, form; similar), of Germanic origin. Functions as a suffix-forming adjective meaning "resembling or characteristic of".