You're hearing the turbo. Was this a used car? If so it may have had the resonator delete modification done by the previous owner.
Not really, you might see a little burst, feel it too. It is a tiny turbo designed to provide boost at the RPM you have mentioned.Okay, so that sound is normal. Good to know. Does that RPM look normal?
Now with a check engine light you should take it in for service. That car should still be under the B2B warranty (depending on exact initial purchase date) and will definitely be under the power train warranty. You shouldn't hear a "constantly revving" sound. You didn't say which trim you have but the RPMs you reported are normal for the LT and LTZ. The ECO MT should be at 2000 RPM at 65 MPH.It?s not high pitched. It just sounds like it?s constsntly revving...