This chapter introduces the general analytic theory of one-dimensional sound propagation in ducts and presents acoustic models for uniform, non-uniform and inhomogeneous ducts with hard or finite impedance walls and parallel sheared mean flow.

Chapter 11 describes calculation of the sound pressure level at a point in the acoustic field of an in-duct source. Insertion loss of a silencer is shown to be represented approximately by source-independent parameters under certain conditions. The discussion encompasses multi-modal sound propagation and radiation and the ASHRAE method of silencer sizing in ventilation and air distribution systems.

This chapter describes the basic analytic concepts and operations which are invoked throughout the book. Mathematical models of sound wave motion in ducts come from the solutions of the linearized forms of the basic fluid dynamic equations of unsteady fluid flow in frequency and wavenumber domains. The process of linearization is discussed in depth and the frequency and wavenumber transformations are defined rigorously. A quantity that is often of interest in duct acoustics is the acoustic power transmitted in a duct. Calculation of time-averaged acoustic power transmitted in ducts is described a unified manner. Finally, we describe the mathematical link with the analyses presented in the book and linear system dynamics. These topics are collected in this preliminary chapter as primer and also to avoid interruption of the continuity of discussions on the principal subjects.

In most duct systems, propagation of duct-borne sound terminates with a duct which opens to an exterior environment. Chapter 9 describes modeling of open ends of ducts and the acoustic field radiated from an open end. This enables acoustic model of a duct system to be extended from the source to the receiver.

In Chapters 3 to 7, the fluid is assumed to be inviscid. Effects of the viscosity and thermal conductivity of the fluid are considered in this chapter. The analysis is based on the low-reduced frequency theory and includes applications to catalytic converter and particulate filters.

Chapter 7 describes modal acoustic models of several coupled duct configurations. The acoustic models described in this chapter extend the one-dimensional area change, junction and perforate elements described in Chapters 3 to three dimensions.

Some coupled-duct configurations occur recurrently in practical systems. In view of the conditions of continuity and compatibility of the acoustic fields, ducts may or may not be connected as individual units. In this chapter we present one-dimensional intermediate acoustic models for basic coupling configurations such as area changes and junctions, and continuous and discrete acoustic models for packs of coupled perforated ducts. These are multi-port elements and they can be connected at their ports to the one-dimensional duct elements given in Chapter 3.