While watching a Schlieren video of a hand clapping, I noted a very distinct difference between a sound wave and a puff of air, which were both created by a hand clapping. What is the difference between a puff of air and a sound wave regarding creation and propagation?
In the video, it appears that some of the energy goes into the sound wave and some of the energy goes into the puff. Is there a principle that governs the distribution of impact energy between oscillation (sound) and pushing (puff?)
Newton's laws for air imply the wave equation, but are not equivalent to it. If air was described by the wave equation and nothing else, then any disturbance would travel at the speed of sound. What set of equations can you write that describes both sound and macroscopic motion at the same time, and what dimensionless parameters specify their relative importance?
For example, one might think that a very low frequency disturbance would be likely to create a "wind". On the other hand, the "pop" heard when you say "p" into a microphone without a pop shield doesn't sound like a super low frequency, yet I suspect that the purpose of the pop shield is to slow down the puff.