Lecture Notes on Acoustics and Noise Control

Description

This textbook provides a guide to the fundamental principles of acoustics in a straightforward manner using a solid foundation in mathematics and physics. It is designed for those who are new to acoustics and noise control, and includes all the necessary material for a comprehensive understanding of the topic. It is written in lecture-note style and can be easily adapted to an acoustics-related one semester course at the senior undergraduate or graduate level. The book also serves as a ready reference for the practicing engineer new to the application of acoustic principles arising in product design and fabrication. Preface Objectives of the Book Style Prerequisites The Big Picture Contents Chapter 1: Complex Numbers for Harmonic Functions 1.1 Review of Complex Numbers 1.2 Complex Numbers in Polar Form 1.3 Four Equivalent Forms to Represent Harmonic Waves 1.4 Mathematical Identity 1.5 Derivation of Four Equivalent Forms 1.5.1 Obtain Form 2 from Form 1 1.5.2 Obtain Form 3 from Form 2 1.5.3 Obtain Form 4 from Form 3 1.6 Visualization and Numerical Validation of Form 1 and Form 2 1.7 Space-Time Harmonic Functions Expressed in Four Equivalent Forms 1.8 Homework Exercises 1.9 References of Trigonometric Identities 1.9.1 Trigonometric Identities of a Single Angle 1.9.2 Trigonometric Identities of Two Angles 1.10 A MATLAB Code for Visualization of Form 1 and Form 2 Chapter 2: Derivation of Acoustic Wave Equation 2.1 Euler´s Force Equation 2.2 Equation of Continuity 2.3 Equation of State 2.3.1 Energy Increase due to Work Done 2.3.2 Pressure due to Colliding of Gases 2.3.3 Derivation of Equation of State 2.4 Derivation of Acoustic Wave Equation 2.5 Formulas for the Speed of Sound 2.5.1 Formula Using Pressure 2.5.2 Formula Using Bulk Modulus 2.5.3 Formula Using Temperature 2.5.4 Formula Using Colliding Speed 2.6 Homework Exercises Chapter 3: Solutions of Acoustic Wave Equation 3.1 Review of Partial Differential Equations 3.1.1 Complex Solutions of a Partial Differential Equation 3.1.2 Trigonometric Solutions of a Partial Differential Equation 3.2 Four Basic Complex Solutions 3.3 Four Basic Traveling Waves 3.4 Four Basic Standing Waves 3.5 Conversion Between Traveling and Standing Waves 3.6 Wavenumber, Angular Frequency, and Wave Speed 3.7 Visualization of Acoustic Waves 3.7.1 Plotting Traveling Wave 3.7.2 Plotting Standing Wave 3.8 Homework Exercises Chapter 4: Acoustic Intensity and Specific Acoustic Impedance 4.1 Pressure-Velocity Relationship 4.1.1 Pressure-Velocity Relationships for BTW 4.1.2 Pressure-Velocity Relationships for BSW 4.1.3 Pressure-Velocity Relationships in Complex Function Form 4.2 RMS Pressure 4.2.1 RMS Pressure of BTW 4.2.2 RMS Pressure of BSW 4.3 Acoustic Intensity 4.3.1 Acoustic Intensity of BTW 4.3.2 Acoustic Intensity of BSW 4.4 Specific Acoustic Impedance Expressed as Real Numbers 4.4.1 Specific Acoustic Impedance of BTW 4.4.2 Specific Acoustic Impedance of BSW 4.5 Specific Acoustic Impedance Expressed as Complex Numbers 4.5.1 Issues with Real Impedance 4.5.2 Definition of Complex Impedance 4.6 Computer Program 4.7 Homework Exercises 4.8 References 4.8.1 Derivatives of Trigonometric and Complex Exponential Functions 4.8.2 Trigonometric Integrals Chapter 5: Solutions of Spherical Wave Equation 5.1 Spherical Coordinate System 5.2 Wave Equation in Spherical Coordinate System 5.3 Pressure Solutions of Wave Equation in Spherical Coordinate System 5.4 Flow Velocity 5.4.1 Flow Velocity in Real Format 5.4.2 Flow Velocity in Complex Format 5.5 RMS Pressure and Acoustic Intensity 5.6 Specific Acoustic Impedance 5.7 Homework Exercises Chapter 6: Acoustic Waves from Spherical Sources 6.1 Review of Pressure and Velocity Formulas for Spherical Waves 6.2 Acoustic Waves from a Pulsating Sphere 6.3 Acoustic Waves from a Small Pulsating Sphere 6.3.1 Near-Field Solutions of a Small Spherical Source (kr 1) 6.3.2 Far-Field Solutions of a Small Spherical Source (kr 1) 6.4 Acoustic Waves from a Point Source 6.4.1 Point Sources Formulated with Source Strength 6.4.2 Flow Rate as Source Strength 6.4.3 Point Source in an Infinite Baffle 6.5 Acoustic Intensity and Sound Power 6.6 Computer Program 6.7 Project 6.8 Objective 6.9 Homework Exercises Chapter 7: Resonant Cavities 7.1 1D Standing Waves Between Two Walls 7.2 Natural Frequencies and Mode Shapes in a Pipe 7.3 2D Boundary Conditions Between Four Walls 7.3.1 2D Standing Wave Solutions of the Wave Equation 7.3.2 2D Nature Frequencies Between Four Walls 7.3.3 2D Mode Shapes Between Four Walls 7.4 3D Boundary Conditions of Rectangular Cavities 7.4.1 3D Standing Wave Solutions of the Wave Equation 7.4.2 3D Natural Frequencies and Mode Shapes 7.5 Homework Exercises Chapter 8: Acoustic Waveguides 8.1 2D Traveling Wave Solutions 8.1.1 Definition of Wavenumber Vectors 8.1.2 Wavenumber Vectors in 2D Traveling Wave Solutions 8.2 Wavenumber Vectors in Resonant Cavities 8.3 Traveling Waves in Resonant Cavities 8.4 Wavenumber Vectors in Acoustic Waveguides 8.5 Traveling Waves in Acoustic Waveguides 8.6 Homework Exercises Chapter 9: Sound Pressure Levels and Octave Bands 9.1 Decibel Scale 9.1.1 Review of Logarithm Rules 9.1.2 Levels and Decibel Scale 9.1.3 Decibel Arithmetic 9.2 Sound Pressure Levels 9.2.1 Power-Like Quantities 9.2.2 Sound Power Levels and Decibel Scale 9.2.3 Sound Pressure Levels and Decibel Scale 9.2.4 Sound Pressure Levels Calculated in Time Domain 9.2.5 Sound Pressure Level Calculated in Frequency Domain 9.3 Octave Bands 9.3.1 Center Frequencies and Upper and Lower Bounds of Octave Bands 9.3.2 Lower and Upper Bounds of Octave Band and 1/3 Octave Band 9.3.3 Preferred Speech Interference Level (PSIL) 9.4 Weighted Sound Pressure Level 9.4.1 Logarithm of Weighting 9.4.2 A-Weighted Decibels (dBA) 9.5 Homework Exercises Chapter 10: Room Acoustics and Acoustical Partitions 10.1 Sound Power, Acoustic Intensity, and Energy Density 10.1.1 Definition of Sound Power 10.1.2 Definition of Acoustic Intensity 10.1.3 Definition of Energy Density 10.2 Absorption Coefficients, Room Constant, and Reverberation Time 10.2.1 Absorption Coefficient of Surface 10.2.2 Room Constant 10.2.3 Reverberation Time 10.3 Room Acoustics 10.3.1 Energy Density due to an Acoustic Source 10.3.2 Sound Pressure Level due to an Acoustic Source 10.4 Transmission Loss due to Acoustical Partitions 10.4.1 Transmission Coefficient 10.4.2 Transmission Loss (TL) 10.5 Noise Reduction due to Acoustical Partitions 10.5.1 Energy Density due to a Partition Wall 10.5.2 Sound Pressure Level due to a Partition Wall 10.5.3 Noise Reduction (NR) 10.6 Homework Exercises Chapter 11: Power Transmission in Pipelines 11.1 Complex Amplitude of Pressure and Acoustic Impedance 11.1.1 Definition of Complex Amplitude of Pressure 11.1.2 Definition of Acoustic Impedance 11.1.3 Transfer Pressure 11.2 Complex Acoustic Impedance 11.3 Balancing Pressure and Conservation of Mass 11.4 Transformation of Pressures 11.5 Transformation of Acoustic Impedance 11.6 Power Reflection and Transmission 11.6.1 Definition of Power of Acoustic Waves 11.6.2 Power Reflection and Transmission Coefficients of One-to-One Pipes 11.6.3 Simplified Cases of Power Reflection and Transmission in One-to-One Pipes 11.6.4 Special Case of Power Reflection and Transmission: One-to-One Pipes 11.7 Numerical Method for Molding of Pipelines 11.8 Computer Program 11.9 Project 11.10 Homework Exercises Chapter 12: Filters and Resonators 12.1 Pressure in a One-to-Two Pipe 12.1.1 Equivalent Acoustic Impedance of a One-to-Two Pipe 12.2 Power Transmission of a One-to-Two Pipe 12.2.1 Power Reflection and Transmission of a One-to-Two Pipe 12.2.2 Special Case of Power Reflection and Transmission: A One-to-Two Pipe with No Returning Waves 12.3 Low-Pass Filters 12.4 High-Pass Filters 12.5 Band-Stop Resonator 12.6 Numerical Method for Modeling of Pipelines with Side Branches 12.7 Project 12.8 Homework Exercises Nomenclature Appendices Appendix 1: Discrete Fourier Transform Discrete Fourier Transform Fourier Series for Periodical Time Function Formulas of Discrete Fourier Series Appendix 2: Power Spectral Density Power Spectral Density Accumulated Sound Pressure Square Sound Pressure Level in Each Band References Index