Thanks for taking the time to ask your question. Here is the Toyota Repair manual for the P/S pump replacement...
What part of the vehicle schematic do you need? Engine, Charging system...
Yes. Most often when we have this problem that you are describing, it is bacause of a loose belt (no enough tension to keep it from slipping---that is what is causing the noise) or the quality of the belt itself. Some lesser quality belts are too thin and will slip no matter how tight you get them.
Also make sure that there is no oil or residue on the belt causing it to slip.
P.S. Here is a cut and paste from an article...
Serpentine belts are a great invention but unfortunately they drive everything on a modern engine which places a lot of load on them. When your belt displays any of the following:
-squeals when accelerating.-chirps constantly-squeals constantly-squeals when wet or moist outside-squeals when cold-or any combination of the above.The belt must be replaced, but wait... If you replace the belt it may stop for a while but then the noise comes back. This is because the old belt was slipping and has polished the pulleys or "glazed" them. So before you replace that noisy belt scrub all of the pulleys well with a scotch brite pad, or a good wire brush to remove the glaze and rough up the surface. Clean them off with brake cleaner afterward. Belts work by friction so if the surface is polished too much the belt will slip. If you have already put on a new belt and it is making noise, -sorry you must buy a new one again. Slipping on the pulleys will glaze a new belt fast which ruins it. Some people say you can apply brake cleaner etc to a new belt to fix it but that may not work well. If it slips it will just mess up your newly cleaned pulleys and you will have to scrub them up all over again. So do the job right and rough up the pulleys AND replace the belt at the same time.
No, a serpantine belt denotes just 1 belt on the car turning all the pulleys. If I'm not mistaken, your Corolla has 3 belts but either way, a loose belts(one that is slipping) will cause this noise.