Medium whining sound when accelerating?

Over the last 8 months I have been hearing this noise. It only happens when I accelerate. I only notice it once the car is up to temperature and not all the time. It will happen when I am turning or just going straight and at all speeds. But most of the time I am going from 0 or traveling under 40 miles an hour. There are times I can make it happen by getting the car up to a constant speed of about 35 or 40 and hitting the accelerator very gently and the sound will start close to 3,000 RPMs. The sound will quit, and the RPMs will drop down to around 2,000 RPMs and go back up again. But I notice nothing in the actual car acceleration or movement. I feel nothing at all in the transmission or steering wheel. The car continues to go fine, no issues, I have had no problems with the car so far, but the noise continues, and I am afraid of it breaking down. But if I just take it to a dealer or repair shop, I will get hit with some huge bill without knowing the true problem.