Passage of Monochromatic Sound Through a Gas Pipeline Wall

On the basis of a rigorous mathematical description of the motion of monochromatic waves, a method is proposed for determining the acoustic permeability of a wall containing an arbitrary number of layers. The method is based on finding exact distributions for incident and reflected waves in each of the layers under consideration and “stitching” linear combinations of these distributions at all common boundaries of adjacent acoustic zones. As a result, to determine the coefficients of linear representations of solutions, a system of algebraic equations is obtained, which can be solved in any and standard way. The study completes the enumeration of all frequencies from the considered spectrum. As an illustrative example, the axisymmetric problem of sound output from a single-layer pipe of a gas pipeline is considered.