Question regarding my split exhaust --

Part #46746 in the picture linked here has rusted through just short of
one of the joints and is severed completely.

http://www.autopartswarehouse.com/images/domestic/images/walker/0811.jpg

What's the common name for this piece? Connecting pipe? Some seem to
call it "muffler," though I thought that referred to the tailpipe piece
specifically.

Just trying to read up so I know better what I'm going in to pay for.