Equivalent circuits for conical waveguides
A. H. Benade · The Journal of the Acoustical Society of America · 1988
The acoustical properties of a cone of length L and small-end radius a0 are shown to be representable via an equivalent circuit involving a pair of inertances, a transformer, and a nontapered duct that has the same length and small-end radius as the cone to be represented. This is shunted at the small end by an inertance proportional to x0, which is the distance from this end to the (projected) apex of the cone. At the large end, there is a similar inertance proportional to the apical distance xe=x0+L. This inertance has a negative sign. The nature and correctness of the representation are demonstrated and a number of illustrative examples are presented, including a transformation of a clarinet (which is cylindrical) by means of a vent hole that gives it the basic playing properties of a saxophone (which is conical). The equivalent circuits are easy to calculate with and speak well to the intuition to suggest properties of the cone that are not otherwise very apparent.