When dealing with intense sound waves, things get more interesting.
Waves start to distort as they travel, generating harmonics, 'self-demodulation', and shocks.
While these effects are well studied for underwater applications, such as sonar, there has historically been little research of these phenomena in air. A simple simulation of a nonlinear plane wave is shown below. A very interesting subject which we have had a great deal of success in is the use of the ultrasonic parametric array to create an Audio Spotlight , which uses the nonlinear interaction of ultrasonic beams to generate extremely directive audible sounds.