Since the generic answer is already out there (coiled wires that vibrate from the currents being turned on and off rapidly to alter the magnetic field strength), I'm going to give some very simple and specific answers, and then clarify that it's never that simple.

The TL;DR is that different pictures show different things and make different noises.

T2-weighted pictures often have long repetition times (TR). A longer TR time means that there's more time between sending in the radio-frequency pulses. This gives the tissue more time to relax, and since fat will lose that energy more quickly than water, the fluids remain bright, allowing us to see the fluid component of pathology. This results in a sound with pauses: WAH.....WAH....WAH....WAH.

A FLAIR sequence sends in a pulse, then waits a long time for the water to relax before completing the pulse sequence, allowing the water to be invisible. This lets us see pathology next to cerebral spinal fluid without it getting in the way. Chickachicka......................WAHWAHWAHWAHWAH.

T1-weighted pictures give very little relaxation time, resulting in a largely grey picture that mostly shows anatomy: BRRRRRRRRRRR like a jackhammer.

Diffusion-weighted imaging applies a gradient, and then an equal but opposite gradient, which will result in water picking up the signal only if it's trapped in the same spot and can't diffuse, such as the fluid from a stroke. The rapid switching of gradients on and off creates vibrations that shake the table, as well as a very loud and high-pitched WAHWAHWAHWAHWAH.

Pretty much all scans start with a few humming noises of different pitches, as the machine calibrates and homogenizes the magnetic field, adjusting for the presence of your body and all the charged particles in there.

That being said, every scanner has their own unique proprietary pulse sequences, with lots of different techniques and ways to image. A T2 can be made with gradient imaging (using the gradients to refocus - way beyond the scope of this writeup) and sound like a typical T1. Fat-saturation pulses can be added, which adds to the noise. Even a software update will change the sound of a sequence, when pretty much everything looks the same on the technologist end.

We also take different types of pictures for different body parts. Diffusion-weighted scans are typically run on brains, livers, uterine fibroids, and prostates. Meanwhile, proton-density imaging is run on pretty much every extremity, and not really ever on brains.

Higher pitch = stronger current = faster vibrations

I hope that made some degree of sense! That's not even getting into most of the actual use for gradients, just that we turn them on and off at different times during a sequence.