Obviously you can’t “quiet the noise” unless you do something to stop its production (block or re-route traffic, for example, or muffle each noise producer, or slow the traffic so that the reduced power levels don’t produce noise in the first place, etc.) or block it at the source. Those ideas would work, but they’re obviously impractical for one homeowner to accomplish.
A lot depends on the geography that you have to work with. Without knowing anything about your topography, whether you’re above or below the source of the sound, whether it surrounds you, comes from a single point, etc. you can still build a berm. (Haven’t we had this discussion before?)
Building a berm at the edge of your property would be the single most effective (legal) thing that you could do. (I also like the idea of felling trees across the road, but you’d probably run out of trees before long, even if you weren’t caught and jailed.) Sound levels of the kind produced by traffic simply will not penetrate through several feet of packed earth. The sound waves will hit that barrier, and most of them will be deflected upward. If you’re not in the path of a sound wave, then you won’t hear it. (Air and atmospheric conditions can re-deflect some of the sound back down again, past the berm, so it’s not like you can create an area that is proofed from the traffic noise, but it will be decreased by several orders of magnitude.)
Berms are expensive – relative to the cost of planting common trees – but they are pretty quick to build and they are permanent if designed well and then planted over to retain the soil in place.
There are other conditions, of course, relating to permitting, drainage issues (you don’t want to turn your yard into a pond whenever it rains, for example) and lines of sight / privacy (you may not want as much privacy as it affords), but they are very effective.
You can also consider creating local sounds that are more pleasing to you, which could drown out the traffic sounds: wind chimes, music, songbirds and television can do that.
You might also consider installing better windows. I was amazed at the reduction of exterior sound when I put in new windows on my house several years ago. EDIT: Never mind that last. That won’t help the back yard much, will it?