My 2005 Corolla CE has a high pitched whine when it downshifts to a low speed and also a "whistle-like" sound when I gently depress the accelerator. This doesn't occur until the car is warmed up -- generally after being driven for 10 miles or so. I usually happens in Drive (I have an automatic transmission). The vehicle functions fine, except for this noise that drives me crazy. I took it into the dealer, but they couldn't find it; the rep advised me he was "chasing a ghost"! According to the dealer, it is not the drive train. There is no noise at high speed, just in stop-start traffic, or when the transmission downshifts to a low gear. I hope someone out there has some suggestions. Thanks.