my ps2 still does that sound with non dvd game copies.
like timesplitters 1 or xtremegracing (blue bottom discs)
the way i fix them is by attaching two pieces of scotch tape of the same size(about 1inch is fine) parallel to each other across the middle hole of the disc.
Because blue bottom discs are lighter than dvd-discs, they have problems spinning at the same speed as regular dvd-discs.
The tape makes up for the difference and allows you to play the games perfectly.
drawing:
..___
./ \
| |o| |
.\___/
where the | around the "o" represent the tape
Edit: had to fix the drawing.
Edit: couldnt fix the drawing lol