The Physics of Music and Color: Sound and Light

Preface to the Second Edition
Preface to the First Edition
Note on Problems and Questions
Questions Discussed in This Book
Contents
1 Introductory Remarks
1.1 Two Contrary Attitudes About Science
1.2 A Scene vs. a Painting
1.2.1 The Joy of a Physicist in Looking at a Mathematical Equation
1.3 Two Views on the Creation of a Musical Composition vs. the Discovery of a Law of Physics
The Legend of the Huang Chung: The Ancient Recognition of the Connection Between Numbers and Music
1.4 Outline of the Book
1.5 What About the Sentient Perception of Musicand Color?
1.6 Questions and Problems for Chap. 1
2 The Vibrating String
2.1 Waves Along a Stretched String
2.2 A Finite String Can Generate Music!
2.3 Pitch, Loudness, and Timbre
2.4 The Relation Between Frequency and Pitch
2.5 The Wave Motion of a Stretched Rope
2.6 Modes of Vibration and Harmonics
2.7 The Sine Wave
2.8 The Simple Harmonic Oscillator
2.8.1 The Physical Basis for the Oscillation of a Simple Harmonic Oscillator
2.8.2 The Vibration Frequency of a Simple Harmonic Oscillator
2.9 Traveling Sine Waves
Applications
2.10 Modes of Vibration—Spatial Structure
2.11 The Wave Velocity of a Vibrating String
Application of the Above Relations to the Piano
2.12 SHO vs. Vibrating String
2.13 Stiffness of a String
2.14 Resonance
Digression on the Modes of Two Coupled SHOs
2.15 General Vibrations of a String
2.15.1 Frequency of a Wave with MissingFundamental
2.16 Periodic Waves and Timbre
2.17 An Application of Fourier's Theorem to Resonance Between Strings
Home Exercise with a Piano
2.18 A Standing Wave as a Sum of Traveling Waves
2.19 Terms
2.20 Important Equations
2.21 Problems for Chap. 2
3 The Nature of Sound
3.1 The Air of Our Atmosphere
3.1.1 Pressure
3.1.2 Generating a Sound Pulse
3.1.3 Digression on Pushing a Block of Wood
3.2 The Nature of Sound Waves in Air
3.3 Characterizing a Sound Wave
3.4 Visualizing a Sound Wave
3.5 The Velocity of Sound
3.5.1 Temperature Dependence of Speed of Sound in Air
3.6 Standing Waves in an Air Column
Standing Waves in a Closed Pipe
End Correction for Modes in a Pipe
3.7 Magic in a Cup of Cocoa
3.8 The Helmholtz Resonator
3.8.1 The Physical Basis for the Helmholtz Resonator
Formula for the Frequency of Helmholtz Resonator
Derivation of the Helmholtz Formula
3.8.2 Flutter of Air Through the Window of a Speeding Automobile
3.9 Terms
3.10 Important Equations
3.11 Problems for Chap. 3
4 Energy
4.1 Forms of Energy and Energy Conservation
4.1.1 Fundamental Forms of Energy
4.1.2 ``Derived'' Forms of Energy
4.1.3 The Energy of Cheerios
4.2 The Principle of Conservation of Energy, Work,and Heat
4.2.1 Series of Changes of Forms of Energy
4.3 Energy of Vibrating Systems
4.3.1 The Simple Harmonic Oscillator
4.3.2 Energy in a Vibrating String
4.3.3 Energy in a Sound Wave
4.4 Power
Power of Various Sources of Sound
4.5 Intensity
4.6 Intensity of a Point Source
4.7 Spectral Intensity with Respect to Frequency
4.7.1 White Noise and Pink Noise
4.8 Sound Level and the Decibel System
4.8.1 Logarithms
4.8.2 Sound Level
4.8.3 From Sound Level to Intensity
4.9 Attenuation
4.9.1 Attenuation in Time
4.9.2 Response and Resonance in the Presence of Attenuation
4.9.3 Attenuation of Traveling Waves—Attenuation in Space
4.9.4 Attenuation of Light in a TransparentMedium
4.10 Reverberation Time
4.11 Terms
4.12 Important Equations
4.13 Problems for Chap. 4
5 Electricity and Magnetism
5.1 The Fundamental Forces of Nature
5.2 The Electric Force
5.3 Electric Currents in Metal Wires
5.4 The Magnetic Force
5.5 Characterization of Magnetic Forces
5.6 Is There a Connection Between Electricity and Magnetism?
5.6.1 Action–Reaction Law and Force of Magnet on Current-Carrying Wire
5.7 The Loudspeaker
5.8 The Buzzer
5.9 The Electric Motor
5.10 Force Between Two Wires Carryingan Electric Current
5.11 The Electromagnetic Force and Michael Faraday
5.12 Applications of Faraday's EMF
5.13 A Final ``Twist''
5.14 Action-at-a-Distance and Faraday's Fields
5.15 The Electric Field
5.16 The Magnetic Field
5.17 Magnetic Force on a Moving Charge
5.18 Force Between Two Parallel Wires Carrying Currents
5.19 Generalized Faraday's Law
5.20 What Do Induced Electric Field Lines Look Like?
5.21 Lenz's Law
5.22 The Guitar Pickup
5.23 Maxwell's Displacement Current
5.24 Electromagnetic Waves
5.25 What Is the Medium for Electromagnetic Waves?
5.26 The Sources of Electromagnetic Waves
SUMMARY of Electricity and Magnetism
5.27 Terms
5.28 Important Equations
5.29 Problems for Chap. 5
6 The Atom as a Source of Light
6.1 Atomic Spectra
6.2 The Hydrogen Spectrum of Visible Lines
6.3 The Bohr Theory of the Hydrogen Atom
6.4 Quantum Theory
6.5 Line Width
6.6 Complex Scenarios of Absorption and Emission
6.6.1 Rayleigh Scattering
6.6.2 Resonant Fluorescence
6.6.3 General Fluorescence
6.6.4 Stimulated Emission
6.7 Is Light a Stream of Photons or a Wave?
6.8 The Connection Between Temperature and Frequency
6.9 Terms
6.10 Important Equations
6.11 Problems for Chap. 6
7 The Principle of Superposition
7.1 The Wave Produced by Colliding Pulses
7.2 Superposition of Two Sine Waves of theSame Frequency
7.3 Two-Source Interference in Space
7.3.1 Detecting the Epicenter of an Earthquake or the Location of a Gunshot
7.3.2 Sound Level with Many Sources
7.3.3 Photons and Two-Slit Interference
7.4 Many-Source Interference
7.4.1 Gratings
7.4.2 Diffraction Through a Mesh
7.4.3 X-ray Diffraction Off Crystals
7.5 Terms
7.6 Important Equations
7.7 Problems for Chap. 7
8 Complex Waves
8.1 Beats
8.1.1 Beats of a Tibetan Bell
8.2 AM and FM Transmission
8.3 AM Transmission
8.3.1 Sidebands
8.3.2 AM Demodulation
8.4 FM Transmission
8.4.1 FM Demodulation
8.4.2 Bandwidth Limitation Imposed on FM Radio Frequency Separations
8.5 Spectrogram
8.5.1 Understanding the Content of a Spectrogram
8.5.2 The Short Time Fourier Spectrum
8.5.3 The Relationship of Spectrograms with Measurement and Perception
The Measurement of Frequency
The Perception of Pitch
8.5.4 Spectrogram of the Gravitational Wave (GW) from a Collapsing Binary Neutron Star
8.6 Polarized Light
8.6.1 How Can We Obtain a Beam of PolarizedLight?
Ideal Polarizer
8.6.2 Calcite
8.6.3 Calcite Loop
8.6.4 Polaroid
8.6.5 Series of Ideal Polarizers
8.6.6 Sample Problems
8.6.7 Partial Polarization of Reflected Light
8.6.8 The Polarization of Scattering Light
8.6.9 The Polarizer Eyes of Bees
8.6.10 Using Polarization of EM Radiation in the Study of the Big Bang
8.6.11 Optical Activity
8.6.12 Our Chiral Biosphere
8.7 Terms
8.8 Important Equations
8.9 Questions and Problems for Chap. 8
9 Propagation Phenomena
9.1 Diffraction
9.1.1 Scattering of Waves and Diffraction
9.1.2 Why Is the Sky Blue?
9.2 Reflection
9.3 Reflection and Refractance
9.3.1 The Reflectance for a Light Wave
9.3.2 The Reflectance for a Sound Wave
9.4 Refraction
9.5 Total Internal Reflection
9.6 The Wave Theory of Refraction
9.7 Application to Mirages
9.8 The Prism
9.9 Dispersion
9.9.1 Effect of Dispersion on a Prism
9.9.2 Effect of Dispersion on Fiber Optics Communication
9.10 Lenses
9.10.1 The Converging Lens
9.10.2 Lens Aberrations
9.10.3 Image Produced by a Converging Lens
9.10.4 Magnification
The Real Image of a Converging Lens as a Secondary Object
9.10.5 The Compound Lens
9.10.6 Reversibility of Rays—Interchange of Object and Image
9.10.7 The Diopter
9.10.8 The Diverging Lens
9.10.9 Determining the Focal Length of a Diverging Lens
9.11 The Doppler Effect
9.11.1 Doppler Effect for Waves in a Medium
Case (i): The Source Is at Rest with Respect to the Medium, While the Observer Is Moving with Respect to the Medium
Case (ii): The Source Is Moving with Respect to the Medium, While the Observer Is at Rest with Respect to the Medium
9.11.2 Doppler Effect for Electromagnetic Waves in Vacuum
9.11.3 Applications of the Doppler Effect
9.12 Terms
9.13 Important Equations
9.14 Questions and Problems for Chap. 9
10 The Ear
10.1 Broad Outline of the Conversion Process
10.2 The Auditory Canal
10.3 The Eardrum
10.4 The Ossicles
10.5 Improving on the Impedance Mismatch: Details
10.6 The Cochlea
10.7 Pitch Discrimination
10.7.1 Some Mathematical Details on Pitch vs. the Peak of the Envelope
10.7.2 Mach's Law of Simultaneous Contrastin Vision
10.7.3 Rhythm Theory of Pitch Perception
10.8 Terms
10.9 Problems for Chap. 10
11 Psychoacoustics
11.1 Equal Loudness Curves
11.2 The ``Sone Scale'' of Expressing Loudness
11.3 Loudness from Many Sources
11.4 Combination Tones and the Non-Linear Response of the Cochlea
11.5 The Blue Color of the Sea and Its Connection with Combination Tones
11.6 Duration of a Note and Pitch Discrimination
11.7 Fusion of Harmonics—A Marvel of AuditoryProcessing
11.8 Additional Psychoacoustic Phenomena
11.9 Terms
11.10 Important Equations
11.11 Problems for Chap. 11
12 Tuning, Intonation, and Temperament—Choosing Frequencies for Musical Notes
12.1 Musical Scales
12.2 The Major Diatonic Scale
12.3 Comments Regarding Western Music
12.4 Pythagorean Tuning and the Pentatonic Scale
12.5 Just Tuning and the Just Scale
12.6 The Just Chromatic Scale
12.7 Intrinsic Problems with Just Tuning
12.8 Equal Tempered Tuning
12.9 The Cents System of Expressing Musical Intervals
12.10 Debussy's 6-Tone Scale
12.11 String-Harmonics
12.12 Terms
12.13 Important Equations
12.14 Problems for Chap. 12
13 The Eye
13.1 The Cornea and Lens
13.2 The Iris
13.3 The ``Humourous'' Liquids of the Eye
13.4 The Retina
13.5 Dark Adaptation
13.6 Depth Perception
13.7 Terms
13.8 Problems for Chap. 13
14 Characterizing Light Sources, Color Filters, and Pigments
14.1 Characterization of a Light Beam
14.2 Spectral Intensity
14.2.1 Measurement of Spectral Intensity
14.2.2 Examples of Spectral Intensities
14.2.3 Determining an Intensity from the Spectral Intensity
14.3 Comments on the Two Spectral Intensities
14.4 White Noise
14.5 Color Filters
Stacking Filters (Filters in Series)
14.6 Reflectance
14.7 Pigments
14.8 Summary Comments on Filters and Pigments
14.9 Terms
14.10 Important Equations
14.11 Problems for Chap. 14
15 Theory of Color Vision
15.1 The Three Primary Colors Theory of Color Vision
15.2 Metamers
15.3 Simplification with Just Six Hues
15.4 Exploration of Color Mixing with a Computer
15.5 Introduction to the Chromaticity Diagram
15.5.1 A Crude Chromaticity Diagram—Color Coördinates
15.6 A Standard Chromaticity Diagram
15.6.1 The Calculation of Color Coördinates
15.6.2 Color Coördinates of Butter
15.6.3 Chromaticity Diagram
15.6.4 Primary Units
15.6.5 Mixing Primaries to Produce a Color
15.6.6 Properties of a Chromaticity Diagram
15.6.7 Mixing Two Incoherent Sources of Light
15.7 Using a Different Set of Primaries
15.7.1 General Features of a Different Setof Primaries
15.8 Comments About Tables of Color Matching Functions
15.9 Brightness and the Luminous Efficiency
15.9.1 Luminous Efficacy and Brightness
15.10 The Standard Chromaticity Diagram of the Commission Internationale de l'Éclairage (C. I. E.)
15.10.1 sRGB Primaries
15.11 From Computer RGB Values to Color
15.12 How Many Colors Are There?
15.12.1 Limitations of a Broadened Gamutof a Monitor
15.13 A Simple Physiological Basis for Color Vision
15.14 Color-Blindness
15.15 After-Images
15.15.1 Questions for Consideration
15.16 Terms
15.17 Important Equations
15.18 Problems on Chap.15
Correction to: The Physics of Music and Color: Sound and Light
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A.1 Units
A.2 Order of Magnitude
A.3 Significant Figures
A.4 Relative Changes
A.4.1 Proportionalities
A.5 Problems for Appendix on Numbers
B Symbols
C Powers of Ten—Prefixes
D Conversions
E References for The Physics of Music and Color
F Crude Derivation of the Frequency of a Simple Harmonic Oscillator
G Numerical Integration of Newton's Equation for a SHO
An Improved Approximation
H Magnifying Power of an Optical System
H.1 Image with the Naked Eye and with a MagnifyingGlass
H.2 The Microscope
H.3 Problems on Magnifying Power
I Threshold of Hearing
J Mappings
J.1 MAPPINGS being Central to Organizing HumanExperience
J.2 NUMBERS as a Mapping
J.3 The Concept of TIME as a Mapping
J.4 Mappings as the Essential Goal of Physics
A Final Remark
K The Mysterious Behavior of the Photon
K.1 Experiments with Calcite Crystals
L Fusion of Harmonics: A Marvel of Auditory Processing
L.1 Mathematica File
M Transformation of Primaries
Explicit Expression for the Transformation Matrix U
M.1 Application of the Transformation: Determining an Ideal Set of Primaries
Procedure
M.2 Proof of Eqs. (M.1) and (M.6)
Proof
M.3 Problems on the Transformation of TCMFs
N Pierre-Gilles de Gennes
Index