Analytical Approximations Related to the Kirchhoff Theory of Acoustic Wave Propagation in Long Cylindrical Tubes

A theoretical study is made of the Kirchhoff theory of acoustic wave propagation in long cylindrical tubes with the objective of deriving analytical expressions for the propagation constant by employing an expansion scheme. The only assumption made is that the Stokes layer thickness root v/omega is much smaller than the wave length a/omega and this provides the expansion parameter. Analytical expressions are obtained for the propagation constant without necessity of solving the algebraic and transcendental equations. Explicit results are obtained for the wide tube case and the numerical values are compared with the computed values reported in literature.