2003 BMW 330 Loud humming noise

First some background - the car had a low-engine
sign (yellow light) and was driven for at least 500
miles. We are now hearing rather loud humming
noise that is especially noticeable when it goes
beyond 40 mph.

Revving the engine while idle does not generate
that much noise. Also, when the car is going
downhill at high speed the noise subsides.

We have changed the oil, but have not checked
any other fluids such as transmission.

I hope it is not coming from inside the engine. How
can I rule that out? Where else could it come from?

Thanks in advance for help.