The Acoustic Physics of Horn Loudspeakers
An acoustic horn functions as an acoustic impedance transformer. A raw loudspeaker diaphragm is a high-mass, high-pressure, low-velocity device trying to push ultra-low-density air. Because of this massive impedance mismatch, a direct-radiator speaker converts less than 2% of electrical power into sound.
A horn gradually transforms high-pressure air at the small throat into low-pressure, large-volume air movement at the wide mouth, boosting electro-acoustic efficiency from 2% to over 25% (a +10 to +15 dB gain in sensitivity!).
The Flare Constant and Wavelength Rule
In an exponential horn, cross-sectional area expands according to (S(x) = S_t imes e^{mx}), where the flare rate (m) is strictly tied to the lowest cutoff frequency (f_c):
Below (f_c), acoustic radiation resistance drops to zero and the horn provides zero acoustic loading.
The Critical Mouth Perimeter Dimension
To prevent sound waves from reflecting back down the horn from the mouth (which creates severe comb-filter phase notches and honky coloration), the mouth perimeter must be at least equal to one full acoustic wavelength at cutoff (( ext{Perimeter} ge lambda_c = rac{c}{f_c})).