so, the air gap in a core needs special treatment. if you look at a commercially made inductor or transformer using split cores, they put plastic spacers in the gaps, and then once the construction of it is completed, they soak the whole thing in varnish, which fills any remaining air spaces, and "glues" the whole thing together. this is how they eliminate the noise that they would normally produce because of magnetically induced motion. an old trick was to find the part of he core or winding that was noisy, and stick a wooden toothpick into the noisy area to dampen the noise. there is actually more than one source of noise possible in an inductor or transformer. the pole pieces slapping against each other (if the gap is not filled properly between the pole pieces), the wires in the winding slapping together (yes the magnetic fields around the wires attract and repel each other, or the wires are attracted or repelled by the ferrite core). if the inductor or transformer uses mounting hardware, the hardware can get loose and make noise. i have seen a lot of different method of eliminating noises, the first, as i mentioned being the toothpick trick, or removing the whole device and dipping in varnish. the device could be potted in silicone potting compound. i used to use a compromise method on CRT monitor flyback transformers, and that was to inject silicone glue into the areas most prone to cause noise (one way that worked well was to disassemble the core, and put silicone glue on the pole pieces and spacers, reassemble the core, and use silicone glue to dampen mechanical contact points between the mounting hardware and the core.