'wave-shaped' is a modern English compound formed from 'wave' + 'shaped' (the past-participle/adjectival form of 'shape'). 'wave' originates from Old English, specifically words like 'wafian'/'wæf' where the root meant 'to wave, fluctuate'; 'shape' originates from Old English 'sceppan' (and related forms) where the root meant 'to form, create'.

'wave' developed from Old English 'wafian'/'wæf' (related to Proto-Germanic roots meaning to move or fluctuate); 'shape' developed from Old English 'sceppan' (from Proto-Germanic *skapjaną 'to create, form'). These elements were combined in modern English to form the descriptive compound 'wave-shaped'.

The component 'wave' initially referred to movement or a waving motion and 'shape' referred to forming; combined in modern usage they mean 'having the form of a wave' rather than indicating motion.