Syllabus

The following topics will be covered throughout the semester:

A. Sample Physical Origins of Wave Motion

• Taut String
• Elastic Rod
• Blood Flow in Arteries
• Sound in a Pipe
• Beam on an elastic foundation
• Traffic Flow on a Freeway
• Long Waves in Shallow Seas, Linearization
• Visit to the Nondestructive Evaluation Laboratory

B. One dimensional propagation

• General Solution, Branching of Arteries, Impedance
• Waves in an Infinite Domain, D'Alembert's Theory
• Characteristics
• Semi-infinite Domain and Reflection
• Forced Waves in an Infinite Domain
• String in an Elastic Surrounding, Dispersion
• Group Velocity and Energy Transport
• Transient Dispersion, Method of Stationary Phase
• Method of Stationary Phase
• Scattering and Radiation of Harmonic Waves, Weak Scattering
• Strong Scattering of Long Water Waves by Depth Discontinuity
• Radiation Condition, Green's Function
• General Identities, Green Theorem
• Reflection in a Slowly Varying Medium, WKB Approximation

C. Two dimensional propagation

• Reflection and Transmission of Plane Waves at an Interface
• Angle of Incidence, Reflection coefficient in the Complex Wave
• Elastic Wave in Solid, Governing Equations
• Free Waves in Infinite Space, Plane Elastic Waves
• Reflection of Elastic Waves from a plane boundary
• P and SV waves
• SH Waves
• Scattering of SH waves
• The Optical Theorem on Scattering
• Scattering of SH Waves by a Circular Cavity
• Diffraction of SH Waves by a line crack - Parabolic Approximation
• Rayleigh Surface Waves in a Half Space
• Elastics Waves due to a line load traveling on a the Ground Surface. Supersonic, Transonic, and Subsonic

D. Waves in the sea

• Linearized Equations
• Progressive Waves in Sea of Constant Depth. Dispersion and Flow Field. Particle Orbit and Energy Transport
• Wave Resistance of a Two Dimensional Obstacle
• Narrow banded dispersive waves. The Schrodinger equation for the Wave Envelope.
• Radiation of Surface Waves Forced by an Oscillating Line Pressure on the Surface.
• Kelvin Ship Waves
• Internal Waves in a Stratified Fluid. Dispersion Relation.
• Internal Waves in an Unbounded Fluid, St. Andrew's Cross

E. Dispersive Waves in Random Media

• Localization by Disorder

Depending on class interest and time we may discuss

F. Waves through laminated media

• Effective Equation for Thin Laminates
• Effective Equation for Thick Laminates

or

G. Nonlinear waves

• Traffic Waves. Green and Red Lights.
• Shocks and Traffic Jam
• Bores and Hydraulic Jumps
• Bore from the Breaking of a Dam