A bracket not secured properly, a broken rubber hook or a severely corroded connector can allow a muffler and / or exhaust pipe to vibrate noisily when it is accelerating or driving on uneven roads or even when the car is stopped and the engine is at idle.
A loose muffler can allow excessive movement of the exhaust pipe or other components and increase stress on those parts, so it can become something more than annoying noise if it does not intervene. If the muffler is hanging lower than normal, there is also the risk that it can break completely suddenly, perhaps passing a dump or crossing railroad tracks.
Modern exhaust systems are generally made of aluminized steel or stainless steel, but this does not mean that the parts containing the exhaust components will last forever. Heat, debris, salt on roads and humidity can cause rust formation in the exhaust system. In particular, short frequent trips allow water vapor to gather in this system, which does not receive enough heat to burn it all, allowing condensation and rust formation.
In addition, a hole or stones can do what rust does not do, disconnecting loose exhaust system parts or creating holes in the muffler or other components. Although sometimes the problem of a noisy muffler could be solved by simply clamping a pair of bolts or replacing a broken hook, the corrosion of the muffler or neighboring parts could be serious enough to require them to be replaced by a mechanic.
However, noise from the exhaust system may not be an external problem: diaphragms or other components inside the mufflers may detach and cause internal noise. Additionally, the silencer may not be the only cause, although it is a potential source of strong noise if broken or linted. The exhaust terminals and screws of the exhaust terminals, the thermal screens over catalytic converters and other components may loosen, and the catalytic converters are able to develop noisy internal vibrations when they run badly.