Depends on what kind of noise it is?

Air noise when it runs? Vibration noise?

Any of these and I doubt exterior insulation is going to make much of a difference.

Noise of any kind is typically a "design" problem. That said, noise is a subjective topic. How loud is loud? How noisy is noisy?

What makes up the "design"?:

To many people these things are often ignored, let's just pick a brand we recognize.

Did your previous unit make noise?

Air noise when it runs. It’s a Trane TEM6 variable 4 ton. Previous 30 year old one made noise. I thought newer ones were quieter.

How long ago was it installed?

Sounds like you need to call the installer. However, adding insulation to the unit isn't going to fix air noise problem.

Due to it being in a closet / model # of the unit in question may limit your options.

If your new air conditioner has the same cooling capacity as the former unit, then you should expect a roughly equivalent noise level when the system runs at full capacity-- at least without modifications to the ductwork. That's not the fault of your replacement contractor--most of whom are lucky to replace a unit in kind without some degradation in system performance. In my experience, the more talented HVAC contractors are usually involved in design and installation of HVAC systems in new construction.

For a given air flow, air noise is a consequence of the particular ductwork design and/or installation. Insulation is often used for noise attenuation. It may be installed inside or outside ductwork depending on the type of insulation and the specific application. If the air noise is on the supply side, then a flexible connection between the supply trunk and individual supplies will help to reduce the noise level. You may also wish to consider sound attenuation of the wall between the air handler and bedroom.

In my experience, the more talented HVAC contractors are usually involved in design and installation of HVAC systems in new construction.

LOL, now I've heard it all... the stories I can one day tell.

Then why did the old unit make noise Charles?

So is your proposition to tear the house down the foundation and start over Charles? That's what builders do. Tell me I'm wrong, go ahead.

I totally agree with you, When I sleep, I don't want to hear anything. I paid a big bill to move my air handler from one side of the house (in attic) to another side of the house above the garage (about 50 feet away). luckily the condenser is also far away from my living area (outside of garage). So, I don't know what type of house you have, but if money is not an issue, do it. Also remember, there are lots of duct work involved, not just move the air handler.

The equipment was installed in May of this year. I live in Dallas, TX. The installer came a couple of days ago and run an operational system check. The sound level is more acceptable now. Thanks for all your comments.

About then only thing he could have done to reduce the noise is slow down the blower motor.

Not correct.

@Stax,

I'm curious to learn what you think the tech did to reduce the air noise.