Spring 2016
PHY306: Physics of Wave Motion
http://www.public.iastate.edu/~jgwang/PHYS306-2016/
Lecturer: Dr. JIGANG WANG
Office: Zanffrano 311
Email: jgwang@iastate.edu
Office Hours: Monday 3–4 PM, by appointment
Lectures: T, R 11:00am @ Room 48, Physics
Score breakup:
Homework problems: 15%
In-class Midterm quizzes & participation: 10%
Mid-term exam 30%
Final exam: 45%
Total: 100%
Homework problem Sets:
1-2 problems per week, due every Thursday
Please hand in every Thursday in class
Solutions posted online on Friday night
Late policy: not allowed
Midterm exam: time, room 45
Final exam: time, room 45
Textbooks:
Vibrations and Waves, A.P. French (Norton, 1971)
The Physics of Vibrations and Waves, Fourth, Fifth or Sixth Edition by H.J. Pain
Course Syllabus and Schedule: next page (may vary depending on progress)
Spring 2016
Week 1: Simple Harmonic Oscillators (SHOs) Complex number notation and use of
exponential series, Simple harmonic motion of mechanical and electrical oscillators, Vector
representation, Superpositions of two SHMs, Superposition of two perpendicular SHMs
Week 2: Damped Simple Harmonic Oscillators (SHOs) Damped motion of mechanical and
electrical oscillators, Heavy damping, Critical damping, Underdamped simple harmonic
oscillations, Logarithmic decrement, Relaxation time, Energy decay and Qvalue
Week 3: The Forced Oscillators Variation of displacement and velocity with frequency of driving
force, Frequency dependence of phase angle between force and displacement, Transient and
steady state behaviour of a forced oscillator, Electrical and mechanical impedance, Power
supplied to oscillator, Q-value as a measure of power absorption bandwidth, Q-value as
amplification factor of low frequency response, Effect of transient term
Week 4: Coupled Oscillations Spring coupled pendulums, Normal coordinates and normal
modes of vibration, Matrices and eigenvalues Inductance coupling of electrical oscillators,
Coupling of many oscillators on a loaded string, Wave motion as the limit of coupled oscillations,
Forced coupled oscillators
Week 5: Transverse Wave Motion Particle and phase velocities, The wave equation,
Transverse waves on a string, The string as a forced oscillator, Standing waves on a string of
fixed length, Normal modes and eigenfrequencies, Energy in a normal mode of oscillation,
Group velocity, Dispersion, Bandwidth Theorem, Transverse waves in a periodic structure
(crystal)
Week 6: Longitudinal Waves Wave equation, Sound waves in gases, Energy distribution in
sound waves, Longitudinal waves in a solid, Longitudinal waves in a periodic structure,
Reflection and transmission of sound waves at a boundary
Week 7-8: Electromagnetic Waves Permeability and permittivity of a medium, Maxwell’s
equations, Displacement current, Wave equations for electric and magnetic field vectors in a
dielectric, Energy density of e.m. waves, Electromagnetic waves in a conductor, Effect of
conductivity adds diffusion equation to wave equation, Propagation and attenuation of e.m.
waves in a conductor, Skin depth, Ratio of displacement current to conduction current as a
criterion for dielectric or conducting behavior, Relaxation time of a conductor, Impedance of a
conductor to e.m. waves, Reflection and transmission of e.m. waves at a boundary, Normal
incidence, Oblique incidence and Fresnel’s equations, Reflection from a conductor, Connection
between impedance and refractive index
Week 9: Waves in More than One Dimension Plane wave representation in 2 and 3 dimensions,
Wave equation in 2- dimensions, Wave guide, Reflection of a 2-dimensional wave at rigid
boundaries, Normal modes and method of separation of variables for 1, 2 and 3 dimensions,
Degeneracy, Normal modes in 3 dimensions, Number of normal modes per unit frequency
interval per unit volume, Application to Planck’s Radiation Law and Debye’s Theory of Specific
Heats, Reflection and transmission of an e.m. wave in 3 dimensions, Snell’s Law, Total internal
relaxation and evanescent waves Week 10: Fourier Methods Fourier series for a periodic
Spring 2016
function, Fourier series for any interval, Application to rectangular velocity pulse on a string,
Bandwidth Theorem, Fourier integral of a single pulse, Fourier Transforms
Week 11-12: Interference and Diffraction Interference, Division of amplitude, Fringes of constant
inclination and thickness, Newton’s Rings, Michelson’s spectral interferometer, Fabry–Perot
interferometer, Finesse, Resolving power, Free spectral range, Optical fiber wave guide,
Division of wave front, Two equal sources, Spatial coherence, Dipole radiation, Linear array of N
equal sources, Fraunhofer diffraction, N slits, Missing orders, Transmission diffraction grating,
Resolving power, Bandwidth theorem, Rectangular aperture, Circular aperture, Fraunhofer far
field diffraction
Week 13 Wave Mechanics Historical review, De Broglie matter waves and wavelength,
Heisenberg’s Uncertainty Principle, Schrodinger’s time independent wave equation, The wave
function, Infinite potential well in 1 dimension, Quantization of energy, Zero point energy,
Probability density, Normalization, Infinite potential well in 3 dimensions, Density of energy
states, Fermi energy level, The potential step, The finite square potential well, The harmonic
oscillator, Electron waves in solids, Bloch functions, Kronig–Penney Model, Brillouin zones,
Energy band, Band structure, Phonons
Week 14 Non-linear Waves, Chaos and Solitons Anharmonic oscillations, Nonlinear restoring
force, Forced vibrations, Electrical ‘relaxation’ oscillator, Chaos and period doubling in an
electrical ‘relaxation’ oscillator, Chaos in a non-linear electrical oscillator, Phase space, Chaos
in a forced non-linear mechanical oscillator, Solitons, Solitons and Schrodinger’s equation,
Optical solitons