What in God's name is this sound?
 

This just started happening out of the blue and it's worse when the weather is cold out (around 30* F).

Very heavy vibration and sound when in reverse and the brake pedal is applied.

While driving at low speeds there is a grinding. I feared transmission at first, but it's not a continual grind. It's more of a rotational grind (Grind grind grind grind) as you go faster, so I'm thinking maybe CV Axel, but that doesn't really explain the loud vibration when the brake pedal is pressed, or does it? It sounds like it's maybe coming from the passenger front, but it's so loud I can't really tell.

Video (turn volume up):

F54 Grinding
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I would certainly concentrate on the front CV joints and wheel bearings. Sounds like it was fairly quite, then kicked up as your passenger front went over the speed bump, so front/right being the most likely culprit. Have you been under it to see if you have any torn boots or something loose? In any case, I would get that looked at sooner than later. Good luck and let us know what you find.

I keep leaning towards the CV Axle too. Do you know of any guides on replacing our axles? I replaced one in my Toyota Corolla a long time ago and two on my dad's F150 and that's it. They're usually pretty straight forward, but I just want to make sure I do everything correctly.

Sounds like it gets louder when you press the brake pedal... Have you looked at your brake pads?