So I just put 4.7 gears in my corolla and after I was done I can hear this humming sound from the back I have no interior so I know I will hear the gears but when I get to 40 MPH the humming sound is really loud I drove it around my neighbor hood and I hit 60 and it's just loud humming I even took it up high RPM in first and second nothing broke or anything just really loud humming is that normal???

i dont know about your gearing but with the stock T-50 tranny you hear a loud humming when you are in fifth gear...

Sounds like the backlash or pinion preload might be off. The a professional install the gears?

Humming is usually bearings. If you have a panhard bar and/or 4-links with spherical bearings, they will transmit the sound into the cockpit more than if you have bushings too.

It might be the pinion preload thanks guys I'm look into that today.

accel / decel / neutral
does it make the same consistent through all these stages or only under certain conditions

Only when I'm over 40

okay after 40 mph, will it make the noise consistently or only under deceleration / acceleration

If the sound stays the same whether coasting, accelerating or in between, it's bearings. If it's only under acceleration or coasting, it's gears.