The djembe and the cajon both use the same principle as a bass reflex cabinet (or a guitar, or bass) the Helmholtz resonance of the enclosed volume and port.
https://en.wikipedia.org/wiki/Helmholtz_resonance
The djembe uses a longer duct on the port, the cajon, stringed instruments (and early bass reflex cabinets) generally use only the thickness of the wood as the port length.
A larger enclosed volume (box) has a lower (and louder) resonance than a smaller box.
The larger the port, the higher the tuning. The longer the port duct is, the lower the tuning.
Ports that are shallow (like the cajon) get "blown out" at higher volume, so the sound becomes "thinner" the harder you play. The djembe, having a much larger slug of air in the port, does not sound as thin when played hard.
A horn is an acoustical impedance matching device, effectively turning a small radiating surface into a large one, a "bigger paddle". To go low requires a long horn and a big mouth, and to be louder than a Helmholtz resonator it must be larger.
To support a 77 Hz wavelength, the horn must be 1/4 wavelength long.
Speed of sound is 1130 feet per second, 1130/77 = 14.67 feet. 14.67/4 =3.67 feet (44 inches, 1.129 meters.
The manufacturer "North" made "horn loaded" drums, though they were too short to reinforce the drum head fundamental much, other than on the smaller toms. They were loud, but being made of plastic, they did not have a very harmonically rich sound, the last I recall micing up was about 35 years ago.
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