I have experienced the symptoms you describe when a voice coil has a certain slight rub. The bad sound can be masked when you play loud. In my case it only showed up when I played quietly or when the note decayed down to a low level. The first thing I would do is test the amp with a different set of speakers.
If you don't have another set of speakers then disconnect them one at a time to isolate the bad one. Short across the terminals of the disconnected speaker to damp the cone movement. Otherwise the disconnected speaker could resonanate and still make the sound. This, of course, assumes that they arn't both bad. (Unlikely, but possible)