Anyone can understand than when applying a static force on a membrane, the contained volume of air in the shell will see its pressure rise, and if a vent is present in the shell, this will lead to a flow of air outside the shell (all of you drummers know you can blow a candle close to a snare vent with one good shot)…but this is a « zero hertz » explanation : looking at flow of air from high pressures to low pressures, linked to diminishing or expanding volumes from the deflection of the membranes.
That blow of air coming out of the vent is actually energy lost from an acoustic standpoint as it is airflow, turbulence, ect..
In reality, the membrane vibrates meaning that getting higher (than zero!) in the frequency range will have us looking at other phenomenon : not of the static flow, but the oscillating exchange between velocity and pressure, and propagation of waves in the drum, as well as « coupling » of the air vibrating within the volume and vibration of the membrane itself.
See this port in speaker cabinet design ? it is not just to « ease » the motion of the woofer back and forth through elimination of static pressure rise if the cavity was closed, it is tuned to match the speaker and cavity characteristics and « help » even more at some particular frequencies.
This phenomenon of coupling has been known for many year but only recent computation techniques could lead to its understanding and refining the design of a system especially when the behavior of the membrane is complex (That is, not acting as a rigid piston)
Timpani , are the perfect example of the effect of air coupling: the shape of the bowl (that limits the cavity) will position air resonances that will move up or down membrane harmonics to end up with a number of partial (harmonics) close to a perfect harmonic series (which is not the case on a ideal vibrating membrane in vacuum).
In other words, this complex phenomenon of air coupling turns a non harmonic vibrating element (i.e. « partials » are not following an integer series as in strings or air column) into a pitch distinctive instrument…This is something really effective at first order when it comes to musical instruments !
This being said, as the main sound radiator for a drum is the membrane, you all know that any modification of its design (Tension, number of plies, coating, rings,… any other damping element) will have a direct impact on the sound produced…but then, what about this coupling with the cavity and effect on the membrane response ? how is this handled on drum set instruments today ?
Varying depth of the shell is certainly a major driver, this having a number of other impacts such as changing the baffle effect that has an impact on the radiation in low frequency, and vibration of the shell.
Venting the drum becomes then a major element – if used correctly – to change the membrane behavior and the response of the drum. Our first series of snare drum prototypes are focused on this aspect of sound generation.