There are a couple of reasons why a 2001 Audi would make humming noises from the back while it is being driven. The first thing to check is the tires. If the tires are fine, check the wheel bearings.
Its most likely a wheel bearing, I had the same problem about a year ago.
Possible wheel bearing going bad.
That noise you're hearing is most likely the wheel bearing. The noise stops because the bearing isn't in motion. As soon as you put the wheel in motion the noise returns due to the bearing being bad. It's a common problem across the board on most Audi's!
Some say that you have to remove the clip-on cover at the back first. Believe to be noise guard.
that is probably your electic fuel pump nothing to worry about
The Audi S4 Avant debuted in 2001. In addition, that year Audi launched the Audi A4 (B6) model. Other Audi models were in production, but these 2 launched in 2001.
The 2001 Audi A4 has 20 valves.
The 2001 Audi S8 has 40 valves.
The 2001 Audi A6 has 30 valves.
The 2001 Audi S8 has a V8 engine.
The 2001 Audi A8 has a V8 engine.
The 2001 Audi A8 has 40 valves.