A share of the energy expended when turning a screw in a fluid can be via vibration of the screw's blades, a portion of which is then transferred to the fluid which may respond in various ways upon its absorption of that energy. The energy losses, i.e., those which do not result in the desired fluid movement, are studied by engineers for the purpose of improving the efficiency of the screw device.

In airplane propellers, for example, one need only to compare more modern slower turning, longer, somewhat twisted, propeller blades with those of yesteryear. The dramatic fuel saving improvements in efficiency of the newer blades, in large measure, resulted from eliminating much of the vibration-ally produced audible noise. Examples abound.

Several other allied applications have also advanced, some of which many of us are familiar, i.e., cooling fans on computers and other electronic devices that work in close proximity to acute human hearing. They were not always so quiet. Then there is the sometimes visual or photographic evidence(as well as audible to those able to listen) of the cavitation of screws turning in heavier fluids such as from propellers on motor boats, though I believe this noise is attributed to a compression/decompression phenomenon in the water. Submariners in particular seem very attentive to their prop screw's designs as well as being of great interest to all seagoing folk for fuel and range matters.

It might bear looking deeper into as to whether any ventilation fan manufacturers have judged the ROI from studying and building quieter bladed large ventilation fans is warranted and found that niche of potential value. The efficiency gains may not be of high appeal, but the reduced noise angle might be. With good fortune there may be some large quiet fans available though not likely at large competitive retail outlets. Good luck.

Our fan is Delta Breeze branded. I believe it's 36" in diameter (may be larger but not sure). The fan itself is belt driven and quiet.

The noise is just the air as it's sucked in through the house and into the attic. It's somewhat loud in the same room but you don't really notice it from other rooms.

I don't think you are using it right. If you were noise would not be a factor. They are supposed to be turned on in evening after sunset for 30-45 minutes with the basement or first floor windows open to drawl in fresh cooler air from outside. So you run it before bed, then turn it off. Having a t-stat makes no sense to me and could be dangerous due to negative pressure and gas hot water heater.

There are three things that cause noise.

The air flow across the blades, this can be lessened by blade design and proper ventilation through roof. I'd suggest vents over wirlybirds.

The noise of motor operating.

The vibration of the motor causing noise within the structure of the framing. The trusses and drywall can act just like a speaker and amplify the vibration.

I've never seen a quite one in my life that was mounted to the trusses in the hallway. If you want quite you need the fan located in the attic then ducted to opening in ceiling to eliminate vibration and move the noise of turbulence and motor away from your living space.

2-3sqft of gable venting isn't nearly enough. There is no where for the air the fan is moving to go, that is part of why it is so loud.

A whole house fan isn't really meant to run all the time, just enough to get an air change through the house.

You need to make sure there is somewhere to draw air from, and somewhere for it to go, and really it shouldn't need to run for more than an hour to have done the job. Not on high the whole time either.

Opening windows is part of the equation, one in each room at least.

You don't have half the gable venting to even meet passive air, is there any other venting in the attic? Also, a given sqft of louvered vent only counts for 75% of its area.

Before you replace the fan, you need more vent area up there anyway, or the new one will be pushing air with no where to go as well. If you have more gable area, say on an opposite end of the attic, that is easy and better than holes in the roof.

Just relating my experience...

I have installed several in both new and old houses back in my construction / electrician days but we used the type where you cut out and head off the joist. We always tried to isolate them from the framing with foam board where possible and rubber grommets on the attachment screws.

Had and used them personally for over 30 years...

Put the last one, a 36 inch, in the hallway of our previous home. Wired it on an optional thermostat so it would shut itself off when it cooled the house out to the desired degree at night as we slept. Restart required a manual button push. Also a nice thing was it was two speed. It was MUCH MUCH quieter on low but it was a challenge to keep the shutters balanced to work properly.

I cut out the tiny restrictive wood louvres and added ten foot wide (4/12 pitch roof) aluminum ones on both gables ends of the house for escaping air and in addition I replaced the fine mesh wire screen on them with 1/2 inch hardware cloth for less restriction. That was actually suggested in the instructions and they listed how much additional exhaust space that effectually added. The fan specs will list the required exhaust space, I doubt exceeding the recommended amount would add much if any noticeable quietness.

Do not currently have one... decades of hard work and the good Lords blessings and now I can afford Air Conditioning...