We back up to Belle Meade Circle which is the main street in and out of Piedmont, Woodbury, and Springdale.
We have a good size lawn at the back of the house that buffers us somewhat. The thing is the traffic is not heavy and in the evening practically non-existent.
My neighbors who back right up to the street do not find it a problem.
Like everything else you have to consider in buying a house, noise level is just another. I would be cautious about which street you back onto, and how close to the street the house sits.
IMHO

I'm in a kind of unique situation. My house, in the southern part of Hemingway, actually backs up to CR 466A. The back yard is really deep and there is a big berm, with palm and oak trees and big shrubs along the top of it. Complete privacy. The traffic doesn't bother me, except when I'm outside and a really big noisy truck goes by. Also I only have to maintain part of the yard, the Village does the part next to the street. I love it. Much better than having a house right behind me.