Chapter Four
Acoustic components
Abstract
The acoustic elements—acoustic mass, acoustic compliance, acoustic resistance—are treated in detail. Examples of mixed elements are given. Next come the reflection and radiation of sound—reflection from a plane; radiation from a pulsating sphere; radiation from a monopole source; radiation from a multiple source; radiation from a dipole source; radiation from an oscillating sphere; and radiation from multiple point sources vibrating with different phases. Directivity index is treated next. A section on radiation impedances follows for: pulsating sphere; oscillating sphere; and circular piston. The chapter ends on viscous and thermal losses, particularly in lossy tubes.
Keywords
Acoustic; Compliance; Directivity index; Dynamic density; Impedances; Multiple source; Particle velocity
4.1. Introduction
We have attempted to present the material in different parts of this text in three ways. The first way is in a form where acoustical phenomena can be visualized and thought of in terms, for example, of analogous electrical circuits. This form is found in the first three chapters. The second way is where straightforward mathematical analysis leads to results that are commonly encountered in engineering practice. This form is found in Chapter 7 where ready-made formulas and tables for loudspeaker systems are presented. The third way is where more advanced mathematical analysis or software is necessary to handle complex acoustical problems, such as when the wavelength is no longer much greater than the largest dimension of the physical structure. We will introduce the mathematical tools for tackling such problems in later chapters, starting with lossy tubes in Section 4.22 and a model for an enclosure in Section 7.18.
In this chapter, we will start with the acoustical and mechanical elements that are used to form electromechanoacoustic circuits that, in turn, are used to calculate the performance of loudspeakers, microphones, and acoustic filters. One obvious acoustical element is the air into which the sound is radiated. Others are air cavities, tubes, slots, and porous screens both behind and in front of actively vibrating diaphragms. These various elements have acoustic impedances associated with them, which can, in some frequency ranges, be represented as simple lumped elements. In other frequency ranges, where the length of the tube or cavity is greater than one-sixteenth of the wavelength such that we have to consider axial pressure fluctuations, distributed elements, analogous to electric lines, must be used in explaining the performance of the devices. For example, a two-port network for a tube of any length is given in Section 4.23 together with analogous circuits. When the radius is greater than one-twenty fifth of the wavelength, we effectively have an enclosure and must consider lateral pressure fluctuations. Enclosures are treated in Chapters 7 and 10. This text does not pretend to advance the science of acoustic components to anything approaching a state of completion. Much research remains to be done. Nonlinearities that occur at higher sound levels, such as shock waves and turbulence, are not covered here. It does attempt to interpret the available theories in such a way that the reader can construct and understand the performance of common acoustic devices.
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