Fan Speed

My question is this: Is it normal for the speed of the heater fan to slow down when the car slows down and speed up when you accelerate? This has only happened in past cars I’ve owned when the alternator was going bad? This is a brand new car and before I call to speak to the dealer, need to know if this is normal. Lots of problems with this “new” car and the dealer likes to tell me it’s all in my head and “normal”

well it ain’t normall