If a buzzing noise is coming from the exhaust at different engine speeds and conditions, this is commonly caused by the heat shields on catalytic converters coming loose at points. The buzzing is the metal on metal contact. Installing a large worm clamp around the catalytic converter and heat shield assembly will prevent the noise and secure the shields.Google+
Car Problem Reports
Ford E-250 Buzzing Noise from Exhaust at Different Engine Speeds
Ford E-250 Problem
Super loud rattle on cold start. Inspected converter and exhaust pipe heat shields with no faults. Problem was caused by the exhaust crossover pipe support bracket located at rear of the transmisssion. These brackets incorporate a guillotine type exhaust pipe clamp that had abraded due to transmission torquing and rust. Removed bracket, noise ended. Will replace with new bracket assembly.