Since we have a fence product that has been used for sound barriers I often get asked by homeowners as to why they cannot just plant trees and accomplish the same thing. I get it. Most trees are much easier to look at than a man-made fence. However, to effectively use trees as a noise barrier (reduce the noise by 5 dB) you would need 30 meters (98 feet) of dense vegetation. Therefore, trees do not provide any meaningful noise abatement, but can provide psychological relief.
Planting rows of hedges and/or trees can define a space as well as give you the privacy you are seeking even though sound will not be minimized. Cutting off the line-of-site is usually the first goal of any natural hedge. Make sure you select the right plants that will grow tall enough to eliminate site lines. The density will depend on the plant and how close you place them. Always check the recommendations for the optimum planting conditions.
There are many people, including myself, that enjoy the privacy and peacefulness a backyard can provide. Just make sure you understand what the objective is for your barrier. If you are just worried about minimizing line-of-site options natural vegetation can work. However, sound barriers exist for a reason because you need the physical material properties to reflect or absorb the sound. This way you can have the backyard that provides the peace and tranquility you are searching for.