1994 Toyota Corolla could my wterpump be failing

First thing is check to see if you can narrow the location down a little. With hood open have engine running and see if there is a definate area the noise is comming from.

I tcould be a few things, look ar the belt routing diagrams to the left of this post. The problem could be from a bearing in the altinator, belt tensioner r pulley, water pump, a/c pump. When you step on the gas and the sound seems to go away It would sound like the belt tensioner pulley. You can try something to get a better idea of where it is coming from. Use a piece about 2 ft long of old garden hose. Put a funnel on the end so the hose fits around the hose. Be careful, with the engine running place the hose side on each part, keeping clear of the belt itself. With the funnel part close to your ear you will be able to tell what the noise is coming from. As I said before keep the hose away from the belt while the engine is running. Once we find out what is making the noise we can figure where to go next about getting it fixed.