Sound is a form of mechanical energy because the source of sound is vibration. Mechanical energy consists of gravitational potential energy and kinetic energy. Vibrating particles have kinetic energy which is a form of mechanical energy.
Sound energy is a form of mechanical energy. It does not produce or come from heat, so it can'y be thermal, there are no chemicals envolved so it's not chemical, it isn't energy associated with electric and magnetic fields so it's not electromagnetic, and does not require any nuclear fission so it's not nuclear.