Tweeter speaker enclosure size and material
You aim to work at sound wavelengths about one inch. High efficiency cabinet would need a horn and matching structure &quot;pressure chamber&quot; at the throat side of the horn. The pressure chamber should be so small that no standing wave could fit into it. The dimensions (=far too big) of your speaker make this impossible, it is already its own cabinet.
I guess you are going to produce intolerable sound and you want to make the effective distance as long as possible. In that case you can try to use the speaker  as a radiator in front of a big parabolic reflector. That's like the radiator horn in old style microwave radar antennas. Narrow beam projects the soundwave to much smaller area than the speaker alone would do. In the middle of the beam you get the same effect as the radiation power was increased.
The apparent power increasing factor (with properly designed and built reflector) that you can expect is (A/B)^2 where A is the diameter of your reflector and B is the diameter of your speaker. This assumes that the beam of your speaker is already so narrow that nearly all of the acoustic power from the speaker meets the reflector. The formula is taken from a book which presents coarse formulas for radar antennas.
About the attenuation: Air isn't frictionless, it has viscosity. Stoke's law gives a rule for attenuation vs distance  in free air. https://en.wikipedia.org/wiki/Stokes%27s_law_of_sound_attenuation It states that energy loss due the viscosity grows as the frequency increases.
How long your sound will reach? Impossible to say even if I knew what's the acoustic output power, how it's directed and what level is considered as &quot;vanished&quot;. I guess you  operate near the ground so ground and all kind of obstacles cause scattering and absorbtion which can only be measured &quot;on site&quot;. Wind and temperature variations make their own effects. If you are lucky they can increase the effective distance.