2024 | Book

# Physical Approach to Engineering Acoustics

Author: Ronald N. Miles

Publisher: Springer International Publishing

Book Series : Mechanical Engineering Series

2024 | Book

Author: Ronald N. Miles

Publisher: Springer International Publishing

Book Series : Mechanical Engineering Series

This updated edition adds new material on the acoustics of mufflers and ducts, including a new analysis on sound propagation in a duct having a cross sectional area that varies in the direction of the duct length. The textbook retains its class-tested fundamentals of engineering acoustics and examination of in-depth concepts within the domains that apply to reducing noise, measuring noise, and designing microphones and loudspeakers. The book particularly emphasizes the physical principles used in designing miniature microphones. These devices are used in billions of electronic products, most visibly, cell phones and hearing aids, and enable countless other applications. Distinct from earlier books on this topic that take the view of the electrical engineer analyzing mechanical systems using electric circuit analogies. This text uses Newtonian mechanics as a more appropriate paradigm for analyzing these mechanical systems and in so doing provides a more direct method of modeling. Written at a level appropriate for upper-division undergraduate and graduate courses, and enhanced with end-of-chapter problems and MatLab routines, the book is ideal as a core text for students interested in engineering acoustics in ME, EE, and physics programs, as well as a reference for engineers and technicians working in the huge global industry of miniature microphone design.

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Abstract

In the following, we will give a very brief introduction to methods used to analyze acoustical signals. This topic on its own constitutes a huge field and one can devote a lifetime to mastering it. Much current research in acoustics involves the creation of algorithms for compressing digitized acoustical signals to facilitate their transmission and storage. A large community of researchers devote their efforts to the analysis of speech signals to enable more efficient and effective means of human–machine and human–human communication.

Abstract

Sound in air that we hear with our ears consists of minute fluctuations in the ambient atmospheric air pressure. If we limit our attention to one dimensional spaces (like inside a narrow tube), we can write down a model for the fluctuating sound pressure. It helps to think of the total air pressure, P(t) as the sum of the static, ambient pressure \(P_0\) and the minute acoustic fluctuation, p(t), \(P(t)=P_0+p(t)\). Of course, if the pressure changes at a point in space, even by a tiny fluctuating amount, we would also expect the density (or total mass of the molecules of the gas for a given volume) to also change depending on the change in pressure.

Abstract

The transmission of sound through walls and barriers is an extremely important topic for noise control engineers. In this chapter we examine the basic principles of how sound passes through walls. The primary physical characteristics that influence sound transmission through walls are studied, including the importance of mass and how the bending rigidity degrades the transmission loss at higher frequencies. Because walls can be fairly complicated constructions, the use of transfer matrices is introduced to enable the prediction of sound transmission loss in walls having multiple layers.

Abstract

The transfer matrix analysis of the transmission through walls as discussed in Chap. 3 is readily adaptable to the analysis of mufflers. This approach will enable us to construct models of muffler and/or duct systems having nearly arbitrary complexity. In the following, we will examine several key muffler components using transfer matrices. A very common muffler construction is the expansion muffler, which consists of a section of a pipe or duct that has an increased cross-sectional area. To develop a transfer matrix model of this we will use three transfer matrices, one for each of the junctions at the ends of the muffler and one for the section between each junction.

Abstract

In the following we will examine the radiation of sound in three dimensions. We will first write the basic equations for the sound field in three dimensions and then consider radiation from a simple point source of sound. We will then extend our study of the radiation from a simple point source to explore sound radiation and reflection in a wide range of acoustic spaces.

Abstract

In the following we will outline the use of computer-aided design models for the analysis of complicated acoustic spaces. The overall goal is to solve the acoustic wave equation for the domain and satisfy the boundary conditions when the geometry is considerably more complicated than can be properly accommodated in analytical solutions. In many studies of sound fields that rely on computational approaches such as the finite element or boundary element methods, the most cumbersome task is in properly describing the geometric details of the domain and boundary conditions. Having the geometry described in a computationally convenient way, the formulation and solution of the equations can be relatively straightforward. The main goal of the following is to provide a brief introduction to the process for formulating and numerically solving the equations based on a geometric description that is readily available through the use of common software used in computer-aided design.

Abstract

While the integral equation approach of determining the sound field described in the previous sections is very general and applicable to a wide range of domain shapes, it rarely leads to equations that are simple enough to provide insight into the nature of the sound field; the results must be obtained numerically. For harmonic sound fields, when the amplitude of the pressure is examined as a function of frequency, one often finds sharp peaks and dips that are very similar to those due to resonances in vibrating structures.

Abstract

The analytical methods of the previous chapters enable predictions of the sound field in an enclosure accounting for numerous geometric and material details of the boundary conditions. In practice however, many acoustical spaces of interest have far too many geometric complexities to permit meaningful predictions of a sound field. In this case, rather than perform painstaking, detailed estimates of the field, it often suffices to estimate the spatial average of the field due to changes in some global, or average acoustical features of the space. For example, it is often extremely important to be able to estimate how the average sound levels in a space will be affected by changes in the average sound absorption on the surfaces. The ability to perform this sort of rough estimate can provide valuable guidance in designs and gives much needed insight without the burden of complicated mathematics.

Abstract

There are many situations where we are interested in the sound field in the vicinity of small objects. This often requires us to account for the viscosity of the medium. This greatly complicates the relationship between fluid velocity near solid obstacles and the fluctuating pressure. In the following, the differential equations for acoustic fluctuations in a viscous fluid are presented. Obtaining solutions to these equations can provide endless challenges. Here we solve them for some specialized situations that are relevant for acoustic sensing.

Abstract

Acoustic sensors normally consist of two essential elements: (1) a mechanical structure that is intended to respond to the minute fluctuations in the medium in a sound field and (2) a means of transducing that response into an electronic signal. In this chapter, we will mainly concentrate on the analysis and design of a suitable structure to respond to these small motions of the medium. The problem of transducing that motion into an electronic signal will be considered in Chap. 11.

Abstract

Chapter 10 was concerned mainly with the mechanical response of a sensing element to sound. In the following, we focus on the problem of how to convert that mechanical motion into an electronic signal. Because the mechanical sensing element must normally be very compliant, the design of the electronic transduction can result in significant forces applied that has a marked influence on the sensor motion. As a result, great care must often be taken to ensure that the transduction system leads to the desired performance.

Abstract

The vast majority of microphones that are produced each year utilize capacitive sensing either through the use of a charged electret material or an applied bias voltage. The design of these microphones, in essentially all cases, relies on simple formulas to estimate the capacitance of parallel plate electrodes. This greatly limits the designs to follow the ubiquitous parallel plate configuration, with all of its common design challenges. In an attempt to overcome this limitation, in the following we review the basic principles of sensing charge and examine a capacitive sensing geometry that overcomes several of the common limitations encountered in capacitive microphone design. Our approach follows that described in [1], which presents an electrostatic sensing scheme that results in a minimum of electrostatic force and stiffness on the moving electrode.

Abstract

There are many situations where it is desirable to estimate values of a finite set of complex parameters to describe devices and systems in acoustics. Methods for the identification of the essential parameters of dynamic systems have been pursued for numerous decades and many review articles and excellent dissertations are available on this subject [1‐10]. Despite the ‘maturity’ of this field, it remains extremely challenging. Some of the algorithms that are available in widely-used software (such as the System Identification Toolbox in Matlab) fail to succeed in identifying the parameters of relatively simple systems [4]. Sekine et al. [11] successfully identified the two lowest modes in a positioning system for a laser but the third mode posed challenges and ‘improvements of the identification accuracy of the 3rd resonance ‘will be a future work.’