Nondissipative Lumped Elements

Abstract

Abstract The goal of this chapter is to start applying the laws of hydrodynamics to acoustics. By applying these laws to some simple acoustical networks, we can begin to develop our understanding of their meaning, as well as exploit their broad utility. We start by ignoring dissipation and by choosing acoustical elements that are small compared to the wavelength of sound. In this nondissipative lumped-element approximation, the continuity equation leads us to the definition of an acoustical compliance (or gas stiffness) that plays the same role as a capacitor in alternating current (AC) electrical circuit theory or a spring in the theory of mechanical vibrations. Under those same approximations, the Euler equation leads to the definition of an acoustical inertance, which is equivalent to an inductor in the electrical analogy, or a mass in the theory of mechanical vibrations. The combination of an acoustical inertance and acoustical compliance is called a Helmholtz resonator. The DeltaEC software is introduced to model such acoustical networks. Because DeltaEC includes dissipation, it provides benchmark results that can be compared to the calculations based on dissipative hydrodynamics in the following chapter.