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MRI machines can be loud because of the vibrations of metal coils inside the machine that create a strong magnetic field. These coils, called gradient coils, are located within a large magnetic field and rapidly switch between positive and negative electrical currents when large amounts of electricity pass through them. This rapid change in currents creates a Lorentz force on the coils, which causes them to vibrate and bang together, producing loud noises that can reach up to 100 decibels. The noise level during active scanning is similar to that of a jackhammer at a construction site.
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So aside from the really strong main field, the MRI needs to switch around really strong auxiliary magnetic fields to focus on what specific areas are being scanned.
Changing magnetic fields cause various metal bits to shrink and expand a bit, and the coils themselves also experience force that causes them to shrink/expand/shift a bit.
It’s the same reason transformers and power supplies hum and whine, just louder and with more interesting variation based on the scan pattern.
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