In a manner so loud or overwhelming that it nearly or completely prevents hearing; extremely loudly.
From 'deafening' (adjective) + '-ly' suffix converting adjectives to adverbs. The base comes from the verb 'deafen' with '-ing' to make an adjective.
'Deafeningly quiet' is a brilliant oxymoron in English—the word itself is so associated with overwhelming volume that describing silence as 'deafeningly quiet' means an absence so complete it's almost shocking!
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