Understanding Acoustics
Understanding Acoustics
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了解声学
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发表时间：
2020
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通讯作者：
Steven L. Garrett
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作者：
Steven L. Garrett
2017年，我（作者B.E.A.）开始定期教授一门关于振动和流体的课程。本课程的前半部分涵盖了质量-弹簧系统、弦、棒、膜和板的振动。课程的后半部分涵盖了平面和球面波的流体声学，声辐射，反射和传播，以及管道中的波。多年来，本课程一直使用Kinsler等人的《声学基础》。2017年春天，美国声学学会（Acoustical Society of America）邀请我评论加勒特（Garrett）的第一版《理解声学》（Understanding Acoustics）。我同意了，认为这本书涵盖了这门课的主题，这给了我一个机会来决定加勒特的书是否适合我。在审查了这本书之后，我采用了它（关于选书过程的更多信息写在参考文献2中）。加勒特的第二版《理解声学》有大量的纹理解释和大量的主题，包括783页。它的优势在于它涵盖了广泛的主题，并围绕方程的发展进行了许多概念性的讨论。这本书的章节主要分为两类：振动和流体中的波。主题覆盖的广度与Kinsler等人的《声学基础》非常相似，但Garrett在Kinsler等人的基础上提供了额外的例子和纹理解释。《理解声学》的一些主要优点是，它是最近出版的，第二版是免费的，在全球范围内都可以下载，这要感谢Veneklasen基金会。这本书是写给物理或工程，高级本科生或研究生观众。学生应该熟悉偏微分方程和复数。第一版中的许多错误已在第二版中得到纠正。第一章提供了泰勒级数、傅立叶合成、复数（或Garrett所说的“方便数”）、单位和误差分析的背景数学处理。第2-6章包括振动材料。深入讨论了“简单”谐振子，包括阻尼振荡器、驱动振荡器、谐振、质量因子和耦合振荡器。加勒特经常加入对振荡器的独特分析，如确定振荡器中波的特征速度，维里定理，瑞利方法，摆的绝热不变性，摩擦阻尼，锁相，以及对动圈扬声器的扩展。耦合振子的极限情况为他的弦理论章节提供了一个很好的过渡。他提供了一个深入的讨论波在弦和图像源创建的边界。他包括了音乐和声和音阶的扩展。在前一章中，他包括了更深入的主题，如点质量扰动和非均匀张力，然后是力驱动弦和位移驱动弦。在过渡到杆和板中的波之前，他提供了深入的弹性介绍，并推导出各种弹性模量。他甚至讨论了屈曲、扭转和螺旋弹簧、粘弹性、复模量和橡胶弹簧。关于杆的一章讨论了通常的纵向、扭转和弯曲波和边界条件。但它也包括独特的主题，如石英晶体微天平、声波打桩和共振超声光谱，从测量的共振频率中提取材料特性。最后，通过对膜和板的振动分析来总结振动章节。讨论了矩形膜和圆形膜中的模态，并给出了模态密度、模态简并、绝热不变性与模态相似度的关系、环形膜和传声器隔膜的扩展等附加主题。他对盘子的处理仅限于夹紧的圆形盘子，但学生们被介绍到盘子的复杂性。第7-15章包括流体材料中的波（尽管Garrett将第15章中的非线性声学分类为扩展章）。在介绍波动方程之前，《理解声学》有几个详细的章节。它从理想气体定律和流体力学开始，考虑微观模型、热力学过程、比热、纳维-斯托克斯和熵。然后加勒特引入了集总流体元素作为描述一维波的先驱。显然，他们的想法是用一种类似于通常用来建立弦中波动方程的方法来建立流体中的波动方程。从一系列耦合的质量和弹簧开始，在有无限个连接的质量和弹簧的极限情况下，离散质量系统变成了一个连续的弦系统。Garrett花了整整一章讨论声质量和弹簧，并向读者介绍了用于一维系统热力学建模的DELTAEC建模软件。然后讨论了耗散流体力学，其中引入了热和粘性边界层损失。在三个关于流体运动的背景章节之后，第10章处理一维流体中的波，包括驻波，驱动系统和结。接下来的一章是关于层状流体介质中的反射和透射以及斜入射，以及恒定声速梯度下的折射。第12章深入研究辐射和散射，考虑单极子、相单极子、偶极子、平动球偶极子、线阵列和挡板活塞。扩展主题对多极扩展，麦克风，声纳浮标，和游泳膀胱也包括在内。他的3-D外壳章节介绍了室内声学和统计能量分析的关键概念。这是对模态密度、漫射场、临界距离和施罗德频率等概念的一个很好的、虽然简短的介绍。还分析了圆柱形和球形外壳，这在室内声学教科书中通常没有涉及。最后，波导结束本章讨论相速和群速、倏逝波、驱动波导和损耗。第十四章回到声音传播中的损耗，尽管现在是在自由空间中。经典的声音衰减与气体、气体混合物、淡水和盐水中的分子松弛损失一起被引入。波导中的传输损耗与量子力学的一些扩展一起被处理。这本书的最后一章是关于非线性声学的。本章的前半部分涵盖了波浪陡增、激波形成和谐波产生等常见主题。他还介绍了非线性声学的各种主题，如参数阵列、共振模式转换和辐射压力的悬浮。这本书的一个独特之处在于加勒特的幽默、轶事、历史见解和个性，这在大多数枯燥的教科书风格中是不典型的。从他的半鼓“所罗门”问题（他声称所罗门王发明了这个问题，理查德·费曼喜欢玩这个问题），到他介绍的“加勒特第一几何定律”，即看起来相似的角度是相似的，到他加入了一个狗身体形状的喇叭作为紧凑源的例子，再到费曼关于用法国曲线重新教授麻省理工学院学生切线概念的故事，加勒特的幽默出现在各个地方。他的个性体现在他的实验延伸、幽默轶事和对流行文化的参考。为了帮助说明
In 2017, I (author B.E.A.) started regularly teaching a course on vibrations and fluids. The first half of this course covers vibrations of a mass-spring system, strings, bars, membranes, and plates. The second half of the course covers fluid acoustics of plane and spherical waves, sound radiation, reflection and transmission, and waves in ducts. For many years Fundamentals of Acoustics by Kinsler et al. was used for this course. In the spring of 2017, the Acoustical Society of America asked me to review the first edition of Understanding Acoustics by Garrett. I agreed, thinking that this book covered the right topics for this course and that this would give me the opportunity to decide if Garrett’s book was a good fit or not. After reviewing the book, I adopted it (more information on that book selection process is written in Ref. 2). Garrett’s second edition of Understanding Acoustics has a lot of textural explanations and a large quantity of topics covered, comprising 783 pages. Its strength is that it covers a wide variety of topics and has many conceptual discussions surrounding the development of equations. The book’s chapters are mainly divided into two categories: vibrations and waves in fluids. The breadth of the topic coverage is very similar to that of Fundamentals of Acoustics by Kinsler et al. but Garrett provides additional examples and textural explanations beyond that of Kinsler et al. Some major advantages of Understanding Acoustics are that it was published more recently and the second edition is available for free, with downloadable access available worldwide, thanks to the Veneklasen Foundation. The book is written for physics or engineering, advanced undergraduate or graduate student audiences. Students should have familiarity with partial differential equations and complex numbers. Many errors in the first edition are now corrected in the second edition. The first chapter provides a background mathematical treatment of Taylor series, Fourier synthesis, complex numbers (or “convenience numbers” as Garrett refers to them), units, and error analysis. Chapters 2–6 comprise the vibrations material. An in-depth discussion of the “simple” harmonic oscillator is given, including the damped oscillator, the driven oscillator, resonance, quality factor, and coupled oscillators. Garrett often adds in unique analyses of the oscillator such as determining a characteristic speed of waves in the oscillator, the virial theorem, Rayleigh’s method, adiabatic invariance of a pendulum, frictional damping, phase locking, and an extension to moving-coil loudspeakers. The limiting case of coupled oscillators provides a nice transition into his String Theory chapter. He provides an in-depth discussion of waves in strings and image sources created by boundaries. He includes extensions to musical consonance and scales. As in the previous chapter he includes deeper topics on strings such as point mass perturbations and nonuniform tension, followed by both the force driven string and the displacement driven string. Before transitioning to waves in bars and plates he provides an in-depth introduction to elasticity and derives various elastic moduli. He even discusses buckling, torsional and coil springs, viscoelasticity, complex moduli, and rubber springs. The chapter on bars goes over the usual longitudinal, torsional, and flexural waves and boundary conditions. But it also includes unique topics like the quartz crystal microbalance, sonic pile driving, and resonant ultrasound spectroscopy to extract material properties from measured resonance frequencies of a bar. Finally, the vibrations chapters are concluded with an analysis of membranes and plates. Modes in rectangular and circular membranes are discussed but additional topics on modal density, modal degeneracy, the relationship of adiabatic invariance to mode similarities, annular membranes, and an extension to microphone diaphragms is given. His treatment of plates is limited to a clamped circular plate, but students are introduced to the complexities of plates. Chapters 7–15 comprise the waves in fluids material (though Garrett classifies the nonlinear acoustics in chapter 15 as an extensions chapter). Understanding Acoustics has a few detailed chapters before introducing the wave equation. It starts with ideal gas laws and hydrodynamics, considering microscopic models, thermodynamic processes, specific heat, Navier-Stokes, and entropy. Garrett then introduces lumped fluid elements as a precursor to describing one-dimensional waves. Apparently, the thinking was to develop the equations for waves in fluids using an approach that is similar to one usually used to develop the equations for waves in strings. Start with a series of coupled masses and springs, and in the limit that you have an infinite number of these connected masses and springs, the system of discrete masses becomes a continuous string system. Garrett spends a whole chapter discussing acoustical masses and springs and introduces the reader to the DELTAEC modeling software used for thermodynamic modeling of 1-D systems. Dissipative hydrodynamics are then discussed, where thermal and viscous boundary layer losses are introduced. After three background chapters on motion in fluids, chapter 10 deals with waves in one-dimensional fluids, including standing waves, driven systems, and junctions. This is followed by a chapter on reflection and transmission in layered fluid media and for oblique incidence, and on refraction with constant sound speed gradients. Chapter 12 dives into radiation and scattering, considering monopoles, inphase monopoles, dipoles, the translational sphere dipole, line arrays, and the baffled piston. Extensions to topics on multipole expansion, microphones, sonobuoys, and swim bladders are also included. His 3-D enclosures chapter introduces key concepts in room acoustics and statistical energy analysis. It is a good, albeit brief introduction to the ideas of modal density, diffuse fields, the critical distance, and the Schroeder frequency. Cylindrical and spherical enclosures are also analyzed, which are not typically covered in room acoustics textbooks. Finally, waveguides finish off this chapter discussing phase and group speed, evanescent waves, driven waveguides, and losses in them. Chapter 14 returns to losses in sound propagation, though now in free space. Classical sound attenuation is introduced along with molecular relaxation losses in gases, gas mixtures, fresh water, and salt water. Transmission loss in waveguides is treated along with some extensions to ideas in quantum mechanics. The final chapter in the book is on nonlinear acoustics. The first half of the chapter covers the usual topics of wave steepening, shock wave formation, and harmonic generation. He also introduces various topics in nonlinear acoustics such as the parametric array, resonant mode conversion, and levitation from radiation pressure. One unique aspect to the book is the inclusion of Garrett’s humor, anecdotes, historical insights, and personality, which is not typical in most dry textbook styles. From his half-drum “Solomongo” problem that he claims King Solomon invented and Richard Feynman enjoyed playing (complete with an altered photo of Feynman), to his introduction of “Garrett’s First Law of Geometry” that angles that look alike are alike, to his inclusion of a dog-body shaped loudspeaker as an example of a compact source, to Feynman’s story about re-teaching MIT students the idea of a tangent using a French curve, Garrett’s humor shows up in various places. His personality shows in his inclusion of experimental extensions, humorous anecdotes, and references to popular culture. To help illustrate