Physics of Oscillations and Waves: With use of Matlab and Python

Preface
	Origin
	Scope
	Content
	Intended Audience
	Computer Programs
	Acknowledgements
Contents
1
	1 Introduction
		1.1 The Multifaceted Physics
		1.2 Numerical Methods
			1.2.1 Supporting Material
			1.2.2 Supporting Literature
2
	2 Free and Damped Oscillations
		2.1 Introductory Remarks
		2.2 Kinematics
		2.3 Going from One Expression to Another
			2.3.1 First Conversion
			2.3.2 Second Conversion
			2.3.3 Third Conversion
			2.3.4 Fourth Conversion
		2.4 Dynamical Description of a Mechanical System
		2.5 Damped Oscillations
		2.6 Superposition and Nonlinear Equations
		2.7 Electrical Oscillations
		2.8 Energy Considerations
		2.9 Learning Objectives
		2.10 Exercises
3
	3 Forced Oscillations and Resonance
		3.1 Introductory Remarks
		3.2 Forced Vibrations
		3.3 Resonance
			3.3.1 Phasor Description
		3.4 The Quality Factor Q
		3.5 Oscillations Driven by a Limited-Duration Force
		3.6 Frequency Response of Systems Driven  by Temporary Forces
		3.7 Example: Hearing
		3.8 Learning Objectives
		3.9 Exercises
		Reference
4
	4 Numerical Methods
		4.1 Introductory Remarks
		4.2 Introduction
		4.3 Basic Idea Behind Numerical Methods
		4.4 Euler\'s Method and Its Variants
		4.5 Runge–Kutta Method
			4.5.1 Description of the Method
		4.6 Partial Differential Equations
		4.7 Example of Numerical Solution: Simple Pendulum
		4.8 Test of Implementation
		4.9 Reproducibility Requirements
		4.10 Some Hints on the Use of Numerical Methods
		4.11 Summary and Program Codes
			4.11.1 Suggestions for Further Reading
		4.12 Learning Objectives
		4.13 Exercises
			4.13.1 An Exciting Motion (Chaotic)
5
	5 Fourier Analysis
		5.1 Introductory Examples
			5.1.1 A Historical Remark
			5.1.2 A Harmonic Function
			5.1.3 Two Harmonic Functions
			5.1.4 Periodic, Nonharmonic Functions
			5.1.5 Nonharmonic, Nonperiodic Functions
		5.2 Real Values, Negative Frequencies
		5.3 Fourier Transformation in Mathematics
			5.3.1 Fourier Series
		5.4 Frequency Analysis
		5.5 Discrete Fourier Transformation
			5.5.1 Fast Fourier Transform (FFT)
			5.5.2 Aliasing/Folding
		5.6 Important Concrete Details
			5.6.1 Each Single Point
			5.6.2 Sampling Theorem
		5.7 Fourier Transformation of Time-Limited Signals
		5.8 Food for Thought
		5.9 Programming Hints
			5.9.1 Indices; Differences Between Matlab and Python
			5.9.2 Fourier Transformation; Example of a Computer Program
		5.10 Appendix: A Useful Point of View
			5.10.1 Program for Visualizing the Average of Sin–Cos Products
			5.10.2 Program Snippets for Use in the Problems
		5.11 Learning Objectives
		5.12 Exercises
		References
6
	6 Waves
		6.1 Introduction
		6.2 Plane Waves
			6.2.1 Speed of Waves
			6.2.2 Solution of the Wave Equation?
			6.2.3 Which Way?
			6.2.4 Other Waveforms
			6.2.5 Sum of Waves
			6.2.6 Complex Form of a Wave
		6.3 Transverse and Longitudinal
		6.4 Derivation of Wave Equation
			6.4.1 Waves on a String
			6.4.2 Waves in Air/Liquids
			6.4.3 Concrete Examples
			6.4.4 Pressure Waves
		6.5 Learning Objectives
		6.6 Exercises
7
	7 Sound
		7.1 Reflection of Waves
			7.1.1 Acoustic Impedance *
			7.1.2 Ultrasonic Images
		7.2 Standing Waves, Musical Instruments, Tones
			7.2.1 Standing Waves
			7.2.2 Quantized Waves
			7.2.3 Musical Instruments and Frequency Spectra
			7.2.4 Wind Instruments
			7.2.5 Breach with Tradition
			7.2.6 How to Vary the Pitch
			7.2.7 Musical Intervals
		7.3 Sound Intensity
			7.3.1 Multiple Simultaneous Frequencies
			7.3.2 Audio Measurement: The Decibel Scale dB(SPL)
			7.3.3 Sound Intensity Perceived by the Human Ear, dB(A)
			7.3.4 Audiogram
		7.4 Other Sound Phenomena You Should Know
			7.4.1 Beats
			7.4.2 Sound Intensity Versus Distance and Time
			7.4.3 Doppler Effect
			7.4.4 Doppler Effect for Electromagnetic Waves
			7.4.5 Shock Waves *
			7.4.6 An Example: Helicopters *
			7.4.7 Sources of Nice Details About Music and Musical Instruments
		7.5 Learning Objectives
		7.6 Exercises
		References
8
	8 Dispersion and Waves on Water
		8.1 Introduction
		8.2 Numerical Study of the Time Evolution of a Wave
			8.2.1 An Example Wave
		8.3 Dispersion: Phase Velocity and Group Velocity
			8.3.1 Why Is the Velocity of Light in Glass Smaller Than That in Vacuum?
			8.3.2 Numerical Modelling of Dispersion
		8.4 Waves in Water
			8.4.1 Circle Description
			8.4.2 Phase Velocity of Water Waves
			8.4.3 Group Velocity of Water Waves
			8.4.4 Wake Pattern for Ships, an Example
			8.4.5 Capillary Waves
		8.5 Program Details and Listing
		8.6 References
		8.7 Learning Objectives
		8.8 Exercises
		References
9
	9 Electromagnetic Waves
		9.1 Introduction
		9.2 Maxwell\'s Equations in Integral Form
		9.3 Differential Form
		9.4 Derivation of the Wave Equation
		9.5 A Solution of the Wave Equation
		9.6 Interesting Details
		9.7 The Electromagnetic Spectrum
		9.8 Energy Transport
			9.8.1 Poynting Vector
		9.9 Radiation Pressure
		9.10 Misconceptions
			9.10.1 Near Field and Far Field
			9.10.2 The Concept of the Photon
			9.10.3 A Challenge
		9.11 Helpful Material
			9.11.1 Useful Mathematical Relations
			9.11.2 Useful Relations and Quantities in Electromagnetism
		9.12 Learning Objectives
		9.13 Exercises
		Reference
10
	10 Reflection, Transmission and Polarization
		10.1 Introduction
		10.2 Electromagnetic Wave Normally Incident  on An Interface
		10.3 Obliquely Incident Waves
			10.3.1 Snel\'s Law of Refraction
			10.3.2 Total Reflection
			10.3.3 More Thorough Analysis of Reflection
			10.3.4 Brewster Angle Phenomenon in Practice
			10.3.5 Fresnel\'s Equations
		10.4 Polarization
			10.4.1 Birefringence
			10.4.2 The Interaction of Light with a Calcite Crystal
			10.4.3 Polarization Filters
			10.4.4 Polariometry
			10.4.5 Polarization in Astronomy
		10.5 Evanescent Waves
		10.6 Stereoscopy
		10.7 Learning Objectives
		10.8 Exercises
		References
11
	11 Measurements of Light, Dispersion, Colours
		11.1 Photometry
			11.1.1 Lumen Versus Watt
		11.2 Dispersion
		11.3 ``Colour\'\'. What Is It?
			11.3.1 Colourimetry
			11.3.2 Colours on a Mobile Phone or Computer Display
			11.3.3 Additive Versus Subtractive Colour Mixing
		11.4 Colour Temperature, Adaptation
			11.4.1 Other Comments
		11.5 Prismatic Spectra
			11.5.1 A Digression: Goethe\'s Colour Theory
		11.6 References
		11.7 Learning Objectives
		11.8 Exercises
		References
12
	12 Geometric Optics
		12.1 Light Rays
		12.2 Light Through a Curved Surface
		12.3 Lens Makers\' Formula
		12.4 Light Ray Optics
			12.4.1 Sign Rules for the Lens Formula
		12.5 Description of Wavefront
		12.6 Optical Instruments
			12.6.1 Loupe
			12.6.2 The Telescope
			12.6.3 Reflecting Telescope
			12.6.4 The Microscope
		12.7 Optical Quality
			12.7.1 Image Quality
			12.7.2 Angle of View
			12.7.3 Image Brightness, Aperture, f-Stop
		12.8 Optics of the Eye
		12.9 Summary
		12.10 Learning Objectives
		12.11 Exercises
		References
13
	13 Interference—Diffraction
		13.1 The Nature of Waves—At Its Purest
		13.2 Huygens\'s Principle
		13.3 Interference: Double-Slit Pattern
			13.3.1 Interference Filters, Interference from a Thin Film
		13.4 Many Parallel Slits (Grating)
			13.4.1 Examples of Interference from a Grating
		13.5 Diffraction from One Slit
		13.6 Combined Effect
		13.7 Physical Mechanisms Behind Diffraction
		13.8 Diffraction, Other Considerations
			13.8.1 The Arrow of Time
		13.9 Numerical Calculation of Diffraction
			13.9.1 The Basic Model
			13.9.2 Different Solutions
		13.10 Diffraction from a Circular Hole
			13.10.1 The Image of Stars in a Telescope
			13.10.2 Divergence of a Light Beam
			13.10.3 Other Examples *
			13.10.4 Diffraction in Two and Three Dimensions
		13.11 Babinet\'s Principle
		13.12 Matlab Code for Diverse Cases of Diffraction
		13.13 Learning Objectives
		13.14 Exercises
14
	14 Wavelet Transform
		14.1 Time-Resolved Frequency Analysis
		14.2 Historical Glimpse
		14.3 Brief Remark on Mathematical Underpinnings
			14.3.1 Refresher on Fourier Transformation
			14.3.2 Formalism of Wavelet Transformation
			14.3.3 ``Discrete Continuous\'\' Wavelet Transformation
			14.3.4 A Far More Efficient Algorithm
		14.4 Example
		14.5 Important Details
			14.5.1 Phase Information and Scaling of Amplitude
			14.5.2 Frequency Resolution Versus Time Resolution
			14.5.3 Border Distortion
		14.6 Optimization
			14.6.1 Optimization of Frequency Resolution (Programming Techniques)
			14.6.2 Optimization of Time Resolution (Programming Techniques)
		14.7 Examples of Wavelet Transformation
			14.7.1 Cuckoo\'s ``coo-coo\'\'
			14.7.2 Chaffinch\'s Song
			14.7.3 Trumpet Sound, Harmonic in Logarithmic Scale
		14.8 Matlab Code for Wavelet Transformation
		14.9 Wavelet Resources on the Internet
		14.10 Learning Objectives
		14.11 Exercises
		Reference
15
	15 Coherence, Dipole Radiation and Laser
		15.1 Coherence, a Qualitative Approach
			15.1.1 When Is Coherence Important?
			15.1.2 Mathematical/Statistical Treatment of Coherence
			15.1.3 Real Physical Signals
		15.2 Finer Details of Coherence
			15.2.1 Numerical Model Used
			15.2.2 Variegated Wavelet Diagram
			15.2.3 Sum of Several Random Signals; Spatial Coherence *
		15.3 Demonstration of Coherence
		15.4 Measurement of Coherence Length for Light
		15.5 Radiation from an Electric Charge
			15.5.1 Dipole Radiation
		15.6 Lasers
			15.6.1 Population Inversion
		15.7 A Matlab Program for Generating Noise  in a Gaussian Frequency Band
		15.8 Original and New Work, Hanbury Brown and Twiss
		15.9 Learning Objectives
		15.10 Exercises
		Reference
16
	16 Skin Depth and Waveguides
		16.1 Do You Remember …?
		16.2 Skin Depth
			16.2.1 Electromagnetic Waves Incident on a Metal Surface
			16.2.2 Skin Depth at Near Field
		16.3 Waveguides
			16.3.1 Wave Patterns in a Rectangular Waveguide
		16.4 Single-Mode Optical Fibre
		16.5 Learning Objectives
		16.6 Exercises
		References
Appendix
	A Front Figure Details
	Index