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Horn Theory, as it has been developed, is based on a series of assumptions and simplifications, but the resulting equations can still give useful information about the behavior of a horn. The problem of sound propagation in horns is a complicated one, and has not yet been rigorously and analytically solved. In essence, it is a three-dimensional problem, but solving the wave equation in 3D is very complicated, in all but the most elementary examples. In the wave equation for three dimensions, the equation describes how sound waves of very small (infinitesimal) amplitudes behave in a three-dimensional medium (e.g. "air"). In 1919, Webster presented a solution to the problem which was made possible by simplifying equation 1 [See: the very technical Wikipedia article linked below] from a three-dimensional to a one-dimensional problem. He did this by assuming that the sound energy was uniformly distributed as a wave-front issuing perpendicular to the horn axis, and by considering only motion of sound in the axial direction [forward, towards the listener]. The result of these simplifications is the so-called “Webster’s Horn Equation,” which can be solved for a large number of cases. You can use this equation to predict what is going on inside a horn, neglecting the higher order effects, but it can’t say anything about what is going on outside the horn; so it can’t predict directivity, once sound exits the horn.
The Tractrix Theory attempts to address the "shape" and resultant character of the sound, taking into account the nature and shape of the horn itself, and the "tugging" effects of natural forces, such as friction with the air. It provides the seeds for a much more perfected horn behavior, and permits a design that lets you have your cake and eat it, too, as the old saying goes. Much research, both scientific and empirical, has led Charney Audio to its cutting-edge use of modern horn technology. We invite you to Just Hear Everything. Gloriously!
Click HERE for more information regarding the Tractrix Theory.
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