When I start my car there is a whirring slightly metallic sound coming from the front passenger side. It stop when I take take it out of park and put it in drive, but start up again when i accelerate. The sound seems to die down the faster i go. By the time, I am at work the car no longer makes the sound in drive or park. I have the same problem when going home, but the sound isn’t as loud in the evening compared to the mornings, which I think has to do with the temperature.
First check all fluids. Then in the morning when this is happening, turn climate control off. No defrosters, nothing, turn on A.C. If the sound goes away the A.C. pulley is bad. If the sound persists, carefully try and locate the noise from a pulley that the belt(s) ride on. You may want to buy a cheap stethoscope and place it near each pulley to locate the source. Just remember that you are working very closely to dangerously moving parts and the fans can kick on at anytime.