Transmission line coefficients for viscothermal acoustics in conical tubes

Viscothermal acoustic propagation in gases contained rigid straight or conical tubes is considered. Under the assumption that wavelength much larger than both boundary layer thickness and tube radius, pressure flow are shown to be solutions of a pair coupled 1D differential equations, formulated as transmission line equations involving complex loss coefficients. The derivation these coefficients, which usually accomplished cylinders, generalized here geometries. In well-known case circular Zwikker–Kosten (ZK) theory recovered. For cones, expression coefficients derived. It involves complex-order spherical harmonics, instead Bessel functions for makes hydraulic radius appear natural relevant geometrical parameter. We show replacing classical by ZK provides an affordable accurate approximation analytic model derived cones. proposed formulas used compute input impedance cone, compared with 3D reference. ideal setting, using harmonics method accurately approximates full method, allows increase accuracy approximately two orders magnitude theory.