How to make audio using ultasonic transmitters
Actually air is always a nonlinear medium.  It's just that it is only very slightly non-linear so that unless the two interacting sound beams have very high pressure levels, the nonlinear effect is too small to observe. Water has a much higher level of nonlinearity and there are sonar systems (I know because I worked on one) that exploit this effect to generate a very low sidelobe signal at the difference frequency of two very high level higher frequency signals.  In fact, in theory, there are no sidelobes at all. However, the downside is that the efficiency of such a sonar is very low because, even in water, the nonlinear effect is small.  We used high frequency beams (at 98 and 106 kHz) with kilowatts of power to generate a difference frequency (12 kHz) beam at an equivalent level of only a few milliwatts. However the sidelobes were almost nonexistent, something to achieve otherwise.  Also, the size of the transmitting array was much smaller since the array need only transmit at the higher frequencies where the wavelength is much smaller.  These effects have been demonstrated in air but again, since air is less nonlinear than water, the efficiency is very small.