Old English hwisprian "speak very softly, murmur" (only in a Northumbrian gloss for Latin murmurare), from Proto-Germanic *hwis- (source also of Middle Dutch wispelen, Old High German hwispalon, German wispeln, wispern, Old Norse hviskra "to whisper"), from PIE *kwei- "to hiss, whistle," imitative. Transitive sense is from 1560s. Related: Whispered; whispering. An alternative verb, now obsolete, was whister (late 14c., from Old English hwæstrian), and Middle English had whistringe grucchere "a slanderer."
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Harper, D. (n.d.). Etymology of whispering. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/whispering