Pull the doghouse and check the clearance of the exhaust against the doghouse opening or for any other contact with anything, that will certainly make a racket. Is it a stock exhaust? Not just the muffler, but larger pipes?
Iíve got very little clearance with my 4Ē pipes from the turbo on the 7.3, I had some work done where the exhaust flange clamp at the turbo had been loosened up and I noticed a droning afterwards. Once the pipe had heated up and expanded from driving, it made contact with the metal pinch seam along the doghouse opening that created an unusual amplified sounding drone at just the right resonance, I had to loosen the flange clamp and pry the exhaust away just enough from making contact before retightening things. Check clearance and signs of any exhaust contact
'03 Ford E350 7.3L Diesel
(de)SMB'd Custom RB-50
Quigley 4X4 w/Deavers & Agile Offroad's R.I.P. package
CCV High Profile Pop Top