Specifically, the energy that is sound will gradually dissipate into energy that is heat. Brownian motion happens on the microscopic level; we perceive it on the macroscopic level as temperature. Temperature is essentially the combined, average kinetic energy of Brownian motion.

Most types of energy gradually turn into heat, including light, macroscopic kinetic energy, released gravitational potential energy, etc.

If you catch a baseball, the kinetic energy of the baseball turns into heat within your muscles (and skin, in the form of friction between the ball and your hands). If you walk down stairs, the gravitational potential energy that you're releasing turns into heat as well, as friction in your joints. Light shining on your skin turns into heat and warms it, as on a bright and sunny day. The electrical energy of a computer converts largely into heat, hence the need for cooling.

There are also theories that all matter may eventually decay, including all atoms and eventually even protons after 10^34 years (though proton decay has not yet been experimentally observed). https://en.wikipedia.org/wiki/Proton_decay

As someone on Quora wrote, "Heat is energy's final grave". The concept of "heat death of the universe" derives from the idea that, eventually, most forms of energy will decay into heat.