Equivalent Circuit of a Tube or Spring

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Abstract
In the equivalent circuit analysis of acoustical structures, invariably the question arises on how to represent distributed‐constant members with lumped‐parameter electrical components, to a given degree of accuracy. For a tube (or spring), a T‐type configuration, with the arms consisting of inductors each equivalent to 1 2 the total inertance and the center leg, a capacitor equivalent to the total acoustical capacitance predicts the 1 4 ‐wavelength resonance frequency within a 10% error. For shorter wavelengths, an equivalent circuit of equal quality is obtained by treating the tube as n equal segments where n is the number of 1 4 ‐wavelengths of the highest frequency of interest approximating the length of the tube. When n is doubled, the error is reduced to within about 3%.

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