Bonjour a tous: Just saw this thread. Great topic!
In decades of power supply work, a few notes please....
1/ I have never seen a mains transformer with a shorted turn. Still its possible.
The result would be a blown fuse due to the circulating current.
2/ Laminated transformers are usually varnished and clamped. Very old parts can get noisy if the clamp or screws loosen or the varnish deteriorates. Often tightening the bolts will help.
3/ In 1980s HP precision power supplies like 6114A, the dual wdg transformer primary had yellow plastic capacitors , 200V 0.47 uF (noise? Emi?) which buzzed loudly ! Replacing the plastic caps solved the noise!
4/ transformer noise is conducted to the chassis, placing a foam or rubber spaces under the transformer may reduce the sound.
5/ Magnetostriction noise is nonlinear, a function of the flux density.
Cheaper transformers have smaller cores and run at higher B, so less efficient and more noise.
Both are worse as the line voltage increases.
6/ Normal line is specified in each country Tolerance of 7...10% +/- is common. Line crept up over time, eg France was 220V now 240V nom. In USA 100>>110>>117 or 120.
Many countries have much worse line regulation. In the USA we see often 120V, in France, 240.
7/ Nonlinear loads like rectifiers cause high peak to RMS currents, I have not seen quiet transformers become noisy as loaded.
I hope these notes are useful to the OP or others!
Bon Fêtes Noël!
Jon