Abstract
Some authors, writing about brass musical instruments, have loosely used the term “effective length,” usually meaning the length of a cylindrical tube with the same resonance frequencies as a given horn, but possibly with different end conditions. In this paper, an attempt is made to define effective length in a precise way that is still consistent with the intent of previous workers who have used the term. Within the framework of plane-wave horn theory, a nonlinear first-order differential equation is derived that yields effective length as a function of frequency and horn contour. This formulation appears well suited to calculating the effect of small changes in the bore of a brass instrument by using a perturbation technique. The differential equation has been solved for some horn contours resembling brass instruments. The solutions display good qualitative agreement with the effective lengths of actual instruments, determined from measured resonance frequencies.
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