Buzzzzzing Transformers

Transformers buzz when the multiple flat stamped out plates that make up the core holding the wire windings start to come loose from one another. They are formed and then sandwiched together and sometimes metal straps, or only the windings hold them together, but usually a varnish of some type is added to keep them bound tightly together.
The A/C current running through it creates an oscillating magnetic field, and the plates want to move in response to the changing field, hence the buzz.
The only real solution is to replace the transformer. The problem will not 'hurt' anything, a lot of transformers get this problem, but are used for many years afterward. If your unit is still in warranty, you should be elegible for a free replacement. It IS a manufacturing defect.
If your unit is out of warranty, possible super cheap attempts at a solution are to squeeze the plates back together tightly somehow. (any ingeneous folks out there?) and re-varnish them.
Also, have you tried to retighten the bolts holding the offending transformer? ?? 05% chance that will quiet it down, worth a try.

Solid state amps usually have toroidal transformers. If they buzz, I would suspect RCA interconnects, dimmer switches, flourescent lights, and maybe (maybe) the turntable motor. Start by a process of elimination. If the amp by itself (nothing attached) still buzzes, then you may have an ac wiring noise problem or the R/C shunt at the input (if there is one) has a bad cap. Of course, it is possible that the xfmr coupling to the chassis is loose, but both?. BTW, what make amp is it, and what is attached to it and how??

Gs5556, your post motivated me to fix a buzz in my shop stereo. One of my (1980 vintage) PS Model 2 power amps running in mono had a loose transformer mounting screw and a bad electrolytic in the input shunt R/C. A new cap and some duct seal under the transformer got rid of the hum. Now if I could just get rid of the fizzy sound that the same amp has that sounds sort of like pink noise from an FM radio with the tuner being slightly twizzled. Noisy input section transistor maybe? Thanks for any suggestions.

Thank you all for the thoughtful and very informative answers. I am currious, and maybe I should be posting a new thread for the following: I recall having read some years ago about a tweak that a reviewer of "positive feedback" performed on his amp's toroidal transformers. He removed the top holding plates and the screws that hold them to the chassis and just let the tranformers stand in place without any fasteners. He reported that the music was sort of liberated and that detail and inner resolution etc, etc, increased dramatically. Of course he warned that the transformers were loose now and any attempt to move the amps should be done very carefully! or disaster could ensue.
How do you like that?
Ted