- •Preface
- •Objectives of the Book
- •Style
- •Prerequisites
- •The Big Picture
- •Contents
- •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
- •1.8 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
- •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
- •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
- •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
- •4.5.1 Issues with Real 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
- •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
- •5.7 Homework Exercises
- •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
- •6.4 Acoustic Waves from a Point Source
- •6.4.1 Point Sources Formulated with Source Strength
- •6.4.2 Flow Rate as Source Strength
- •6.5 Acoustic Intensity and Sound Power
- •6.6 Computer Program
- •6.7 Project
- •6.8 Objective
- •6.9 Homework Exercises
- •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
- •8.1 2D Traveling Wave Solutions
- •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
- •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
- •9.2.2 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
- •9.5 Homework Exercises
- •10.1 Sound Power, Acoustic Intensity, and Energy Density
- •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
- •10.4.2 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
- •11.1 Complex Amplitude of Pressure and 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
- •11.7 Numerical Method for Molding of Pipelines
- •11.8 Computer Program
- •11.9 Project
- •11.10 Homework Exercises
- •12.1.1 Equivalent Acoustic Impedance of a One-to-Two Pipe
- •12.2 Power Transmission of a One-to-Two Pipe
- •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
Nomenclature1
c |
|
|
wave speed, the speed of sound |
ex, ey, ez |
base vectors of Cartesian coordinates |
||
e |
, e |
, e |
base vectors of spherical coordinates |
bf r |
bθ |
bϕ |
circular frequency |
bfo |
b |
b |
center frequency |
flower |
|
lower limit frequency |
|
fupper |
|
upper limit frequency |
|
I |
|
|
acoustic intensity |
Ia |
|
|
moment of inertia of one particle |
IL |
|
insertion loss |
|
Ka |
|
kinetic energy of one particle |
kexperimentally determined coefficient of air for excess absorption coefficient
k |
wave number |
kx, ky, kz |
components of wave number vector |
Lp |
pressure level |
Lw |
pressure level from direct source |
Lx, Ly, Lz |
dimensions of a rectangular cavity |
ma |
mass of one particle |
NR |
noise reduction |
nx, ny, nz |
components of a unit vector in wave propagation direction |
PSIL |
preferred speech interference level |
Po |
averaged air pressure |
P |
absolute air pressure |
p |
pressure difference (P Po) |
p(x, t) |
one-dimensional pressure function |
p(x, y, z, t) |
three-dimensional pressure function |
1 Capital letter for amplitude and Bold facing for complex number. |
|
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 |
355 |
H. Lin et al., Lecture Notes on Acoustics and Noise Control, |
|
https://doi.org/10.1007/978-3-030-88213-6 |
|
356 |
Nomenclature |
p+() |
forward traveling pressure wave |
p () |
backward traveling pressure wave |
ps() |
standing pressure wave |
Q |
directivity of a source |
Qs |
source strength |
Qρ |
mass flow rate |
R |
room constant |
R |
reflection coefficient; radius |
Rm |
mechanical resistance |
RMS |
root mean square |
r, θ, φ |
spherical coordinates |
S |
cross-section area |
S |
surface area of a room |
SPL |
sound pressure level |
T |
period |
T(t) |
time function |
TL |
transmission loss |
T60 |
reverberation time (decay to 60 dB) |
U |
flow rate amplitude (VS) |
u |
flow rate (vS) |
V |
velocity amplitude; volume of a room |
Va |
volume occupied by one particle |
v |
flow velocity |
vca |
colliding speed of a particle |
vf(x, t) |
one-dimensional flow velocity in x-direction |
! |
flow velocity |
v f ðx, y, z, tÞ |
sound power |
w |
|
X(x) |
space function |
x, y, z |
Cartesian coordinates |
Z, Za |
acoustic impedance (p/u¼p/(vS)¼z/S) |
Zm |
mechanical impedance (pS/u¼ zS) |
z |
specific acoustic impedance (p/v) |
αsound absorption coefficient
αaverage sound absorption coefficient
α0, αtot |
total average absorption coefficient include excess absorption |
|
coefficient |
αex |
excess absorption coefficient |
γratio of specific heat
δtotal energy density
δd |
direct energy density |
δr |
reverberant energy density |
θphase angle
θca |
rotation speed of a particle |
λwave length
Nomenclature |
357 |
ξlocation along the wave number vector
ρinstantaneous mass density of the air
ρ0 |
averaged mass density of the air |
τtransmission coefficient
ϕphase angle
ωangular frequency