Hearing nature sounds does indeed relax people who are stressed. Van Praag and her team report that their “findings may help explain reported health benefits of exposure to natural environments, through identification of alterations to autonomic activity and functional coupling within the DMN [default mode network of the brain] when listening to naturalistic sounds.” Natural sounds that are relaxing include, for example, gently moving water (think: burbling brooks) and leaves rustling in a gentle breeze.
Cassandra van Praag, Sarah Garfinkel, Oliver Sparasci, Alex Mees, Andrew Philippides, Mark Ware, Cristina Ottaviani, and Hugo Critchley. 2017. “Mind-Wandering and Alterations to Default Mode Network Connectivity When Listening to Naturalistic Versus Artificial Sounds.” Scientific Reports, vol. 7, article number 45273.