Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Course Overview

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 (cont.)
  • 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 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


G. Nonlinear Waves

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