There are two main causes of a loud airplane sound: the secondary air pump (electric) and the engine-driven-though-clutch fan.
The relay may fuse on the secondary air pump and cause it to stay on all the time. Unplug the relay to see if it turns off for diagnostics. It will burn out in short order if left to run all the time. It's only supposed to be on for a minute after a cold start to inject air into the primary cats to heat them up faster.
The fan clutch on the front of the engine may sieze up, causing the fan to rotate at water pump speeds all the time. This is even worse as the fan was not meant to go that fast and has been known to explode if it is weak or contacts the shroud due to worn engine mounts. This is easy to identify. At a stop, rev the engine in neutral. If it sounds like it's taking off, then it's this fan and you should change the clutch and fan blades immediately. If it's loud while doing this it also can't be the driveshaft as it isn't moving...