In a recent video by PS Audio/Paul, he mentions the sentiment that many probably share with him, that a loudspeaker driver works by compressing air as it moves outwards. This illustrates perfectly that you can work with loudspeakers for decades without ever understanding how a loudspeaker actually works. As we will see in a minute, there is rarefaction as the driver moves outwards, and compression as it moves inwards.
Let us first discuss why intuition tells us to agree with Paul. It could be that you think about sticking your hand out the car window and feeling the pressure pushing back on your hand, and so there effectively is 'positive' or forwards displacement with your hand to the air molecules resulting in a positive pressure. Or you might think about the driver moving outwards for a positive DC voltage from a battery, and that is what is tripping you up. Or maybe you are thinking about the pressure in an enclosure, not necessarily a loudspeaker but a bike pump, where you push the piston in a 'positive' direction and get a positive pressure. But we are talking about acoustics with wave propagation here, and not fluid flow. And how a driver behaves at DC is not how it behave above its characteristic frequency. And free field is different than an enclosure.
If we look at the pressure generated in free field from a flat piston in a baffle, we can calculate analytically calculate the pressure generated via the so-called First Rayleigh integral [Fourier Acoustics, E.G. Williams].
View attachment 269995
The pivotal point here is the sign on the righthand side. With w(Q) being the outwards displacement in a point Q on the piston, it is clearly seen that for a piston radiating into free space (mass-like impedance), this displacement is in anti-phase with p(P); the pressure in a measurement point P. This is really all we need to see. There, in general, is a 180 degree phase difference between the outwards displacement of a loudspeaker and the resulting pressure. Which of course means that when it moves outwards, defined as a positive displacement, we clearly get a negative pressure!