Do you mean that the audible noise is there when operating on 400 Hz, or that it's there at 50 or 60 Hz now? You are right to suspect the core laminations buzzing. On transformers intentionally built to run well up to 400 Hz, the laminations are usually quite a bit thinner than for 50/60 Hz, so tend to be more pliable and can rattle against each other if anything is too loose. Usually the whole transformer would be vacuum impregnated with some kind of varnish or other goop that damps the motions at all frequencies, but after so many years it can deteriorate or get rusty, or the core mounting may loosen up. This all can happen in a regular 50/60 Hz unit too. Also, a regular unit can work at 400 Hz too, but the core loss goes up, so it would tend to run hotter, and you would want a little derating of thermal specs - usually no big deal.
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You can look at the condition and try tightening or loosening it up first, then look to see if a particular area is emitting most of the power. If it's an E-I core, the corners can be quite tight due to the mounting screws, but the rest in between tends to bow and form gaps that allow motion. Sometimes it can be mostly caused by a gap around a single lamination that's just right to resonate and be irritating. If there's room enough, you can poke around between laminations with a razor blade and maybe find spots where it can jam in and greatly change the sound situation. If you ID any really bad ones, you can jam a paper or plastic shim in there.
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The noise is harmless to the machine, but you can get eddy currents that circulate in and around the chassis depending on the electro-mechanical character and condition of the core mounting scheme, so there can be some signal interference. I wouldn't worry too much about it in this old gear, unless it seriously affects the specs or is very irritating.
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Ed
