Problem with my Civic I don't want happening to my new Z

[CDepp]

Maybe I'm the only one, but there's a odd noise that seems to originate from the passenger's seat during rapid acceleration and taking turns to the point of squealing the tires. It doesn't happen all the time, but the screeching noise is loud and only seems to happen at the worst time, when the fiance is in the car. And, it's not always a screech, sometimes it's a yelp, a squeak, or even a (I know it sounds weird) a crying sound.

It aggravates me because I'm afraid the noise upsets her. Each time I look over to investigate the noise, I can see on her face that she's really upset about the noise.

The reason I bring this up is that I'm getting my first Z on Monday and I want to ensure this noise isn't common with this car as much as I hear it with my Civic. Any suggestions?