In open plan offices there is no silence. Working at home there's no silence.
Headphones offer the only escape. They're also a sign that you are trying to concentrate to discourage those "just a quick word" moments which could easily be covered by an instant message.
For you I'd recommend some ear protectors that one might use when operating power tools :-).
I actually think ear protectors with some bluetooth headphones built in might be the ideal solution :-)