But you do agree that the membrane can be lighter than the total mass of the air it moves.
A confusing statement. In a longitudinal wave (such as a sound wave), molecules of "air" are displaced from a median position by varying amounts producing regions of compression (as the membrane moves forward) and rarefaction (as the membrane moves backwards) along the axis of propagation. The molecules end up where they started once the wave has passed. The wave moves - the air does not.
The very basis of a wave is the transmission of energy without the transport of matter.
I agree that it is desirable to have a membrane with as low a mass as possible without sacrificing stiffness. The thickness achieved in the design you are referring to is amazing.
Regards,