A horn is actually an acoustical transformer. It increases the efficiency of coupling of the impedance of the small mouth (relative to the wavelength of vocal frequencies) to the surrounding atmosphere. It does not "amplify" the vocal power output which is in the microwatt range before and after passing through the horn. By enhancing the coupling efficiency it facilitates projection of the main part of the vocal frequency range. The main frequency range for vocal communication is from about 500 Hz to 3kHz. The wavelength of sound in air is roughly 1 foot at 1kHz.
The other phenomenon exploited by the horn is increasing the directionality of the projected voice. As the outlet aperture of the horn increases, the directionality of the projected voice narrows into a sharper beam.
Decades ago I fabricated a parabolic microphone reflector about 1 meter in diameter to identify sound sources in refineries from overlooking hills for our acoustical consultation practice. Testing the directionality by rotating the microphone and reflector in front of a sound source in an open field, we found that the directionality was very sharp in the multi-kHz range but essentially zero below 1 kHz. Directionality is directly related to "gain" relative to the bare microphone. (Our reflector was used for decades by Yosemite rescue personnel to communicate with climbers stranded on rock faces.)
The conical horn shown in the poster's photo is very inefficient, acoustically. Far more efficient is an exponential flare with the rate of flare directly influencing the lowest frequency that can be propagated efficiently through the horn (and the diameter of the mouth influencing the efficiency of coupling of the low frequencies to the air). That is the reason for the familiar graceful curved appearance of horns on everything from truck and train horns to civil defense alarm horns. Most of the science of horn acoustics was developed subsequent to the use of the simple conical horn shown in the silent movie set.
awright

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