Oh, by the way skhochay, your video - the one you made - on what makes tires noisy is... uhm... it's not really accurate.
You state that there are two things that make a tire noisy...
1. The BFG is "oval" - referring to the footprint, e.g. the center is higher than the sides
2. "But that (referring to the "flat" cooper) doesn't matter. What matters is the wall (referring to the sidewall)... that the BFG has big gaps in the wall."
You're getting close with the second point - the larger voids in the BFG (an AT) are a factor in making the tire louder than the Cooper (a street tire). But, it's not the sidewall that's the primary factor...
The tread pattern and the size of the tire (the amount of air space) are the two primary factors determining how loud a tire is. As the tire rolls, the tread is really "striking" the street. Think of each lug striking the street independently. The larger the lugs and the larger the voids, the more significant those strikes.
Then comes tire size. Each of those strikes reverberates through the large space inside the tire - effectively turning it to a drum. The bigger the tire, the "bigger" the noise. Think of that kid with huge drum in the marching band... ever heard a truck on 44s on the street? Roughly the same sound.
As the tread rolls, it flexes, the lugs strike, air and water are pumped away from the center... this all makes noise. Tire engineers design the treads - ATs and MTs too - to minimize and cancel out those effects. They're getting really good at it too. Older mud terrains were comically loud.