![]() 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 result of these simplifications is the so-called “Webster’s Horn Equation,” which can be solved for a large number of cases. ![]() 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. ![]() In 1919, Webster presented a solution to the problem which was made possible by simplifying equation 1 from a three-dimensional to a one-dimensional problem. 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. 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. The problem of sound propagation in horns is a complicated one, and has not yet been rigorously and analytically solved. 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.
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