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1.
to shut up. usually expressed in the form of a request.
will you put a sock in it? i'm trying to study here.
by themarcuscreature February 10, 2005
 
2.
Currently means "Be Quit" or "Shut up".

Originally meant "Turn the Volume down."

In the days before Electricity there was no Volume Control on a record player (Gramophone) so the only way to reduce the volume down was to "Put a sock" (Or other item) in the speaker to muffle it.
Two kids are playing noisily, and their Dad shouts at them "Put a sock in it you two, I am on the Phone!"
by Dorsai December 20, 2010