MRI scanners are notoriously loud despite not having moving parts other than the table. The commonality here is magnetic coils.
When you run a current through a coil, it creates a magnetic field, which pulls on some metals and any other magnetic coil in the system. Since both MRI scanners and transformers use more than one magnetic coil, they pull on each other. This moves them a bit in place, leading to vibrations the same way striking an object does.
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