To test my belt I had a plant spray bottle adjusted for a fine stream and I sprayed the moving belt a couple of times to see if that had any effect. It did so that is why I figured it was the belt. As for the whirring noise, use a "sounding stick" or mechanics stethoscope to track it down. Be careful near the moving parts!! Don't touch anything moving of course, just put the stick near each possible noise source. Likely candidates are the tensioner, alternator and water pump. Or AC compressor or PS pump maybe.

Mike

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1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra