I can hear the camera in live view...?

I'm new to dslr's and have been using my d5500 for a little while, but last night it was quiet when I was using live view and I can hear the camera making this sorta whirring noise. When I take a picture it kind of revs up and then snaps the shot. If I turn off live view, there's no sound.

Please tell me this is normal.

Is it the sound of autofocus? That can be a whirring sound. It should be similar in viewfinder mode though, but depending on settings and lighting, it might hunt for focus a little bit more in live view, causing extra sound. For a quick test, you could switch your lens to manual focus and see if the sound stops. The only other sound in live view is the extra shutter actuations, it closes, then opens and closes to time the exposure, then reopens to get back to live view. That is a click-clack sound though.

Could be VR kicking in as well - depends on the lens.