The Acoustic Wave Equation and Simple Solutions
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Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
Nonlinear Acoustics Applied to Nondestructive Testing
TO NONDESTRUCTIVE TESTING NONDESTRUCTIVE TO APPLIED ACOUSTICS NONLINEAR ABSTRACT Sensitive nonlinear acoustic methods are suitable But it is in general difficult to limit the geometrical for material characterization. This thesis describes extent of low-frequency acoustic waves. A techni- NONLINEAR ACOUSTICS APPLIED three nonlinear acoustic methods that are proven que is presented that constrains the wave field to useful for detection of defects like cracks and de- a localized trapped mode so that damage can be TO NONDESTRUCTIVE TESTING laminations in solids. They offer the possibility to located. use relatively low frequencies which is advanta- geous because attenuation and diffraction effects Keywords: nonlinear acoustics, nondestructive tes- are smaller for low frequencies. Therefore large ting, activation density, slow dynamics, resonance and multi-layered complete objects can be investi- frequency, nonlinear wave modulation spectros- gated in about one second. copy, harmonic generation, trapped modes, open Sometimes the position of the damage is required. resonator, sweep rate. Kristian Haller Kristian Haller Blekinge Institute of Technology Licentiate Dissertation Series No. 2007:07 2007:07 ISSN 1650-2140 School of Engineering 2007:07 ISBN 978-91-7295-119-8 Nonlinear Acoustics Applied to NonDestructive Testing Kristian Haller Blekinge Institute of Technology Licentiate Dissertation Series No 2007:07 ISSN 1650-2140 ISBN 978-91-7295-119-8 Nonlinear Acoustics Applied to NonDestructive Testing Kristian Haller Department of Mechanical Engineering School of Engineering Blekinge Institute of Technology SWEDEN © 2007 Kristian Haller Department of Mechanical Engineering School of Engineering Publisher: Blekinge Institute of Technology Printed by Printfabriken, Karlskrona, Sweden 2007 ISBN 978-91-7295-119-8 Acknowledgements This work was carried out at the Department of Mechanical Engineering, Blekinge Institute of Technology, Karlskrona, Sweden. -
Waves and Imaging Class Notes - 18.325
Waves and Imaging Class notes - 18.325 Laurent Demanet Draft December 20, 2016 2 Preface In the margins of this text we use • the symbol (!) to draw attention when a physical assumption or sim- plification is made; and • the symbol ($) to draw attention when a mathematical fact is stated without proof. Thanks are extended to the following people for discussions, suggestions, and contributions to early drafts: William Symes, Thibaut Lienart, Nicholas Maxwell, Pierre-David Letourneau, Russell Hewett, and Vincent Jugnon. These notes are accompanied by computer exercises in Python, that show how to code the adjoint-state method in 1D, in a step-by-step fash- ion, from scratch. They are provided by Russell Hewett, as part of our software platform, the Python Seismic Imaging Toolbox (PySIT), available at http://pysit.org. 3 4 Contents 1 Wave equations 9 1.1 Physical models . .9 1.1.1 Acoustic waves . .9 1.1.2 Elastic waves . 13 1.1.3 Electromagnetic waves . 17 1.2 Special solutions . 19 1.2.1 Plane waves, dispersion relations . 19 1.2.2 Traveling waves, characteristic equations . 24 1.2.3 Spherical waves, Green's functions . 29 1.2.4 The Helmholtz equation . 34 1.2.5 Reflected waves . 35 1.3 Exercises . 39 2 Geometrical optics 45 2.1 Traveltimes and Green's functions . 45 2.2 Rays . 49 2.3 Amplitudes . 52 2.4 Caustics . 54 2.5 Exercises . 55 3 Scattering series 59 3.1 Perturbations and Born series . 60 3.2 Convergence of the Born series (math) . 63 3.3 Convergence of the Born series (physics) . -
The Standing Acoustic Wave Principle Within the Frequency Analysis Of
inee Eng ring al & ic d M e e d Misun, J Biomed Eng Med Devic 2016, 1:3 m i o c i a B l D f o e v DOI: 10.4172/2475-7586.1000116 l i a c n e r s u o Journal of Biomedical Engineering and Medical Devices J ISSN: 2475-7586 Review Article Open Access The Standing Acoustic Wave Principle within the Frequency Analysis of Acoustic Signals in the Cochlea Vojtech Misun* Department of Solid Mechanics, Mechatronics and Biomechanics, Brno University of Technology, Brno, Czech Republic Abstract The organ of hearing is responsible for the correct frequency analysis of auditory perceptions coming from the outer environment. The article deals with the principles of the analysis of auditory perceptions in the cochlea only, i.e., from the overall signal leaving the oval window to its decomposition realized by the basilar membrane. The paper presents two different methods with the function of the cochlea considered as a frequency analyzer of perceived acoustic signals. First, there is an analysis of the principle that cochlear function involves acoustic waves travelling along the basilar membrane; this concept is one that prevails in the contemporary specialist literature. Then, a new principle with the working name “the principle of standing acoustic waves in the common cavity of the scala vestibuli and scala tympani” is presented and defined in depth. According to this principle, individual structural modes of the basilar membrane are excited by continuous standing waves of acoustic pressure in the scale tympani. Keywords: Cochlea function; Acoustic signals; Frequency analysis; The following is a description of the theories in question: Travelling wave principle; Standing wave principle 1. -
Nuclear Acoustic Resonance Investigations of the Longitudinal and Transverse Electron-Lattice Interaction in Transition Metals and Alloys V
NUCLEAR ACOUSTIC RESONANCE INVESTIGATIONS OF THE LONGITUDINAL AND TRANSVERSE ELECTRON-LATTICE INTERACTION IN TRANSITION METALS AND ALLOYS V. Müller, G. Schanz, E.-J. Unterhorst, D. Maurer To cite this version: V. Müller, G. Schanz, E.-J. Unterhorst, D. Maurer. NUCLEAR ACOUSTIC RESONANCE INVES- TIGATIONS OF THE LONGITUDINAL AND TRANSVERSE ELECTRON-LATTICE INTERAC- TION IN TRANSITION METALS AND ALLOYS. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-389-C6-391. 10.1051/jphyscol:19816113. jpa-00221175 HAL Id: jpa-00221175 https://hal.archives-ouvertes.fr/jpa-00221175 Submitted on 1 Jan 1981 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE CoZZoque C6, suppZe'ment au no 22, Tome 42, de'cembre 1981 page C6-389 NUCLEAR ACOUSTIC RESONANCE INVESTIGATIONS OF THE LONGITUDINAL AND TRANSVERSE ELECTRON-LATTICE INTERACTION IN TRANSITION METALS AND ALLOYS V. Miiller, G. Schanz, E.-J. Unterhorst and D. Maurer &eie Universit8G Berlin, Fachbereich Physik, Kiinigin-Luise-Str.28-30, 0-1000 Berlin 33, Gemany Abstract.- In metals the conduction electrons contribute significantly to the acoustic-wave-induced electric-field-gradient-tensor (DEFG) at the nuclear positions. Since nuclear electric quadrupole coupling to the DEFG is sensi- tive to acoustic shear modes only, nuclear acoustic resonance (NAR) is a par- ticularly useful tool in studying the coup1 ing of electrons to shear modes without being affected by volume dilatations. -
A Comparison Study of Normal-Incidence Acoustic Impedance Measurements of a Perforate Liner
A Comparison Study of Normal-Incidence Acoustic Impedance Measurements of a Perforate Liner Todd Schultz1 The Mathworks, Inc, Natick, MA 01760 Fei Liu,2 Louis Cattafesta, Mark Sheplak3 University of Florida, Gainesville, FL 32611 and Michael Jones4 NASA Langley Research Center, Hampton, VA 23681 The eduction of the acoustic impedance for liner configurations is fundamental to the reduction of noise from modern jet engines. Ultimately, this property must be measured accurately for use in analytical and numerical propagation models of aircraft engine noise. Thus any standardized measurement techniques must be validated by providing reliable and consistent results for different facilities and sample sizes. This paper compares normal- incidence acoustic impedance measurements using the two-microphone method of ten nominally identical individual liner samples from two facilities, namely 50.8 mm and 25.4 mm square waveguides at NASA Langley Research Center and the University of Florida, respectively. The liner chosen for this investigation is a simple single-degree-of-freedom perforate liner with resonance and anti-resonance frequencies near 1.1 kHz and 2.2 kHz, respectively. The results show that the ten measurements have the most variation around the anti-resonance frequency, where statistically significant differences exist between the averaged results from the two facilities. However, the sample-to-sample variation is comparable in magnitude to the predicted cross-sectional area-dependent cavity dissipation differences between facilities, providing evidence that the size of the present samples does not significantly influence the results away from anti-resonance. I. Introduction ODERN turbofan engines rely on acoustic liners to suppress engine noise and meet community noise Mstandards. -
Acoustic Wave Propagation in Rivers: an Experimental Study Thomas Geay1, Ludovic Michel1,2, Sébastien Zanker2 and James Robert Rigby3 1Univ
Acoustic wave propagation in rivers: an experimental study Thomas Geay1, Ludovic Michel1,2, Sébastien Zanker2 and James Robert Rigby3 1Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab, 38000 Grenoble, France 2EDF, Division Technique Générale, 38000 Grenoble, France 5 3USDA-ARS National Sedimentation Laboratory, Oxford, Mississippi, USA Correspondence to: Thomas Geay ([email protected]) Abstract. This research has been conducted to develop the use of Passive Acoustic Monitoring (PAM) in rivers, a surrogate method for bedload monitoring. PAM consists in measuring the underwater noise naturally generated by bedload particles when impacting the river bed. Monitored bedload acoustic signals depend on bedload characteristics (e.g. grain size 10 distribution, fluxes) but are also affected by the environment in which the acoustic waves are propagated. This study focuses on the determination of propagation effects in rivers. An experimental approach has been conducted in several streams to estimate acoustic propagation laws in field conditions. It is found that acoustic waves are differently propagated according to their frequency. As reported in other studies, acoustic waves are affected by the existence of a cutoff frequency in the kHz region. This cutoff frequency is inversely proportional to the water depth: larger water depth enables a better propagation of 15 the acoustic waves at low frequency. Above the cutoff frequency, attenuation coefficients are found to increase linearly with frequency. The power of bedload sounds is more attenuated at higher frequencies than at low frequencies which means that, above the cutoff frequency, sounds of big particles are better propagated than sounds of small particles. Finally, it is observed that attenuation coefficients are variable within 2 orders of magnitude from one river to another. -
Arxiv:1912.02281V1 [Math.NA] 4 Dec 2019
A HIGH-ORDER DISCONTINUOUS GALERKIN METHOD FOR NONLINEAR SOUND WAVES PAOLA. F. ANTONIETTI1, ILARIO MAZZIERI1, MARKUS MUHR∗;2, VANJA NIKOLIC´ 3, AND BARBARA WOHLMUTH2 1MOX, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy 2Department of Mathematics, Technical University of Munich, Germany 3Department of Mathematics, Radboud University, The Netherlands Abstract. We propose a high-order discontinuous Galerkin scheme for nonlinear acoustic waves on polytopic meshes. To model sound propagation with and without losses, we use Westervelt's nonlinear wave equation with and without strong damping. Challenges in the numerical analysis lie in handling the nonlinearity in the model, which involves the derivatives in time of the acoustic velocity potential, and in preventing the equation from degenerating. We rely in our approach on the Banach fixed-point theorem combined with a stability and convergence analysis of a linear wave equation with a variable coefficient in front of the second time derivative. By doing so, we derive an a priori error estimate for Westervelt's equation in a suitable energy norm for the polynomial degree p ≥ 2. Numerical experiments carried out in two-dimensional settings illustrate the theoretical convergence results. In addition, we demonstrate efficiency of the method in a three- dimensional domain with varying medium parameters, where we use the discontinuous Galerkin approach in a hybrid way. 1. Introduction Nonlinear sound waves arise in many different applications, such as medical ultra- sound [20, 35, 44], fatigue crack detection [46, 48], or musical acoustics of brass instru- ments [10, 23, 38]. Although considerable work has been devoted to their analytical stud- ies [29, 30, 33, 37] and their computational treatment [27, 34, 42, 51], rigorous numerical analysis of nonlinear acoustic phenomena is still largely missing from the literature. -
Physics of Ultrasound TI Precision Labs – Ultrasonic Sensing
Physics of Ultrasound TI Precision Labs – Ultrasonic Sensing Presented by Akeem Whitehead Prepared by Akeem Whitehead Definition of Ultrasound Sound Frequency Spectrum Ultrasound is defined as: • sound waves with a frequency above the upper limit of human hearing at -destructive testing EarthquakeVolcano Human hearing Animal hearingAutomotiveWater park level assist sensingLiquid IdentificationMedical diagnosticsNon Acoustic microscopy 20kHz. • having physical properties that are 0 20 200 2k 20k 200k 2M 20M 200M identical to audible sound. • a frequency some animals use for Infrasound Audible Ultrasound navigation and echo location. This content will focus on ultrasonic systems that use transducers operating between 20kHz up to several GHz. >20kHz 2 Acoustics of Ultrasound When ultrasound is a stimulus: When ultrasound is a sensation: Generates and Emits Ultrasound Wave Detects and Responds to Ultrasound Wave 3 Sound Propagation Ultrasound propagates as: • longitudinal waves in air, water, plasma Particles at Rest • transverse waves in solids The transducer’s vibrating diaphragm is the source of the ultrasonic wave. As the source vibrates, the vibrations propagate away at the speed of sound to Longitudinal Wave form a measureable ultrasonic wave. Direction of Particle Motion Direction of The particles of the medium only transport the vibration is Parallel Wave Propagation of the ultrasonic wave, but do not travel with the wave. The medium can cause waves to be reflected, refracted, or attenuated over time. Transverse Wave An ultrasonic wave cannot travel through a vacuum. Direction of Particle Motion λ is Perpendicular 4 Acoustic Properties 100 90 Ultrasonic propagation is affected by: 80 1. Relationship between density, pressure, and temperature 70 to determine the speed of sound. -
Design and Analysis of a Single Stage, Traveling Wave, Thermoacoustic Engine for Bi-Directional Turbine Generator Integration Mitchell Mcgaughy Clemson University
Clemson University TigerPrints All Theses Theses 12-2018 Design and Analysis of a Single Stage, Traveling Wave, Thermoacoustic Engine for Bi-Directional Turbine Generator Integration Mitchell McGaughy Clemson University Follow this and additional works at: https://tigerprints.clemson.edu/all_theses Part of the Mechanical Engineering Commons Recommended Citation McGaughy, Mitchell, "Design and Analysis of a Single Stage, Traveling Wave, Thermoacoustic Engine for Bi-Directional Turbine Generator Integration" (2018). All Theses. 2962. https://tigerprints.clemson.edu/all_theses/2962 This Thesis is brought to you for free and open access by the Theses at TigerPrints. It has been accepted for inclusion in All Theses by an authorized administrator of TigerPrints. For more information, please contact [email protected]. DESIGN AND ANALYSIS OF A SINGLE STAGE, TRAVELING WAVE, THERMOACOUSTIC ENGINE FOR BI-DIRECTIONAL TURBINE GENERATOR INTEGRATION A Thesis Presented to the Graduate School of Clemson University In Partial Fulfillment of the Requirements for the Degree Master of Science Mechanical Engineering by Mitchell McGaughy December 2018 Accepted by: Dr. John R. Wagner, Committee Co-Chair Dr. Thomas Salem, Committee Co-Chair Dr. Todd Schweisinger, Committee Member ABSTRACT The demand for clean, sustainable, and cost-effective energy continues to increase due to global population growth and corresponding use of consumer products. Thermoacoustic technology potentially offers a sustainable and reliable solution to help address the continuing demand for electric power. A thermoacoustic device, operating on the principle of standing or traveling acoustic waves, can be designed as a heat pump or a prime mover system. The provision of heat to a thermoacoustic prime mover results in the generation of an acoustic wave that can be converted into electrical power. -
Particle Motions Caused by Seismic Interface Waves
Prodeedings of the 37th Scandinavian Symposium on Physical Acoustics 2 - 5 February 2014 Particle motions caused by seismic interface waves Jens M. Hovem, [email protected] 37th Scandinavian Symposium on Physical Acoustics Geilo 2nd - 5th February 2014 Abstract Particle motion sensitivity has shown to be important for fish responding to low frequency anthropogenic such as sounds generated by piling and explosions. The purpose of this article is to discuss the particle motions of seismic interface waves generated by low frequency sources close to solid rigid bottoms. In such cases, interface waves, of the type known as ground roll, or Rayleigh, Stoneley and Scholte waves, may be excited. The interface waves are transversal waves with slow propagation speed and characterized with large particle movements, particularity in the vertical direction. The waves decay exponentially with distance from the bottom and the sea bottom absorption causes the waves to decay relative fast with range and frequency. The interface waves may be important to include in the discussion when studying impact of low frequency anthropogenic noise at generated by relative low frequencies, for instance by piling and explosion and other subsea construction works. 1 Introduction Particle motion sensitivity has shown to be important for fish responding to low frequency anthropogenic such as sounds generated by piling and explosions (Tasker et al. 2010). It is therefore surprising that studies of the impact of sounds generated by anthropogenic activities upon fish and invertebrates have usually focused on propagated sound pressure, rather than particle motion, see Popper, and Hastings (2009) for a summary and overview. Normally the sound pressure and particle velocity are simply related by a constant; the specific acoustic impedance Z=c, i.e. -
Measurements of Acoustic Impedance and Their Data Application to Calculation and Audible Simulation of Sound Propagation
Acoust. Sci. & Tech. 29, 1 (2008) #2008 The Acoustical Society of Japan PAPER Measurements of acoustic impedance and their data application to calculation and audible simulation of sound propagation Teruo Iwase1, Yu Murotuka2, Kenichi Ishikawa3 and Koichi Yoshihisa4 1Faculty of Engineering, Niigata University, 8050 Igarashi 2-no-cho Nishi-ku, Niigata, 950–2181 Japan 2Graduate School, Niigata University, 8050 Igarashi 2-no-cho Nishi-ku, Niigata, 950–2181 Japan 3Oriental Consultants Co. Ltd., Shibuya Bldg. 16–28 Shibuya, Shibuya-ku, Tokyo 150–0036 Japan 4Faculty of Science and Technology, Meijo University, 1–501 Shiogamaguchi, Tempaku-ku, Nagoya, 468–8502 Japan ( Received 20 April 2007, Accepted for publication 17 August 2007 ) Abstract: Acoustic impedance determines the boundary condition of each sound field, but collections of actual values to evaluate sound fields are insufficient. Therefore, measurements of acoustic impedance using a particle velocity sensor were taken on different fields. Such measurement results were used for sound propagation calculations. Frequency characteristics of sound propagation on grass, snow-covered, and porous drainage pavement surfaces showed fair correspondence with field measurement results. Subsequently, fine calculations in the frequency domain were converted to impulse responses for each sound field model. Convolution operations based on the impulse response and on voice, music, and other noise sources readily produced an ideal sound field for the audible sound file. Furthermore, simulations of noise from a car running through a paved drainage area, with noise reduction effects, were attempted as advanced applications. Keywords: Acoustic impedance, Sound propagation, Road traffic noise, Snow field, Drainage pavement, Impulse response, Convolution PACS number: 43.28.En, 43.58.Bh [doi:10.1250/ast.29.21] example, the prediction method for traffic noise has 1.