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When your body is placed inside this big magnetic field, all the hydrogen nuclei begin to spin around. This is what magnets do when they are in a very straight magnetic field, like the one inside an electromagnet. When they spin around, the MRI machine can "listen" to them by tuning in a special radio. How fast they spin around, or the pitch of the "note" they "sing" depends on how strong the magnetic field is.
By turning on other coils inside the big one, the magnetic field is made different at different parts of your body, which causes the hydrogen nuclei to sing different notes depending on where they are. By turning on and off different coils at different times, each nucleus can be made to sing a unique song, depending on where it is located. The computer can then interpret this song to tell where the nuclei are, and constructs an image.
The clicking and banging sounds you hear are the various coils being turned on and off. A wire, in a magnetic field, with electricity going through it feels a force. The coils are in a large magnetic field, and so when they are on they feel a large force. Even though they are held down very tightly they move a little bit, and that's what you hear.
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