SHAPE OF THE HORN
FLARE OF THE HORN
Exponential-Hyperbolic-Parabolic-Bessel-Catenoidal-Conical
The shape of the horn is represented by a mathematical formula that indicates the ratio of the horn’s cross-sectional area at a given distance, from the horn throat. Extensively used shapes are the Catenoidal, Conical, Bessel, Hyperbolic, Parabolic and the most common the Exponential one. These are all families of horns the mouth of which does not end at 90 degrees to their central axis. When the sound waves exit from the mouth of those horns out to space, there is discontinuity. (The sound waves are spherical). Reflections at the mouth travel back to the driver’s diaphragm. From this interaction results parasitic peaks and dips that distort the sound. Therefore the acoustic coupling between horn’s mouth and space is not perfect.
Tractrix-spherical
The TRACTRIX expansion is historically the last horn flare submitted by Paul Voigt in 1926. It is the only horn’s flare whose mouth ends at 90 degrees to its central axis. The effect of this unique termination is the minimum mouth reflections. If you set up the differential equation for the spherical wave fronts traveling down the horn, you end up with the mathematical expansion of the tractrix curve
THE CROSS SECTION OF THE HORN
Rectangular
The rectangular cross section, is the most common shape. The wide angle dispersion, a major specification for theaters, cinemas and Professional Audio applications, is covered by asymmetric, rectangular horns. However the main problem of the rectangular cross section, is the stationary waves between the opposite sides, launching diffraction and turbulence of the sound.
Circular-cylindrical
The cylindrical cross section is the exact mathematical expression of the Exponential, Tractrix and other flares. There are no turbulence of sound waves. Better imaging, undistorted sound with a less narrow beam than rectangular’s cross section.
FLARE-CROSS SECTION COMBINATIONS
Exponential-rectangular
The most common (and vintage) combination of exponential-rectangular shape, is built of wood or aluminum . The majority of listeners relate these horns with the nasal sound known as ‘’horny’’ sound. Their worst critics simulate this nasal sound placing their hands in front of their mouths (parabolic flare), thus distorting their voices. In fact they hear the worst horn shape. The midrange region, which is the most sensitive region to our ears , is distorted. This flare-cross section combination is only acceptable for bass horn applications.
Tractrix-cylindrical
This is the ideal theoretical approach. Even the tractrix-rectangular combination, which is a generous compromising approach, is theoretically and acoustically far beyond. The cylindrical tractrix ideally combines minimum distortions and best imaging. The best horn combination for high end home applications.
