2.062J | Spring 2017 | Graduate
Wave Propagation



Sample Wave Problems

  • Transverse Vibration of a Taut String
  • Longitudinal Vibration of an Elastic Rod
  • Traffic Flow on a Freeway

Problem set 1 out

Sample Wave Problems (cont.)

  • Wave Propagation in Arteries
  • Shallow Water Waves and Linearization
  • Sound in Fluids
  • Flexural Waves in a Beam on an Elastic Foundation

Problem set 1 due

One Dimensional Waves

  • General Solution to Wave Equation
  • Branching of Arteries
  • Waves in an Infinite Domain due to Initial Disturbances
  • Reflection from the Fixed End of a String
  • Forced Waves in an Infinite Domain

Problem set 2 out

One Dimensional Waves (cont.)

  • String Embedded in an Elastic Surrounding
  • Dispersion from a Localized Initial Disturbance
  • Scattering of Sinusoidal Waves
  • General Identities in Scattering by Arbitrary in Homogeneities
  • Refraction in a Slowly Varying Medium

Problem set 2 due

Two Dimensional Waves

  • Reflection and Transmission of Sound at an Interface
  • Equations for Elastic Waves
  • Free Waves in Infinite Space
  • Elastic Waves in a Plane

Problem set 3 out

Two Dimensional Waves (cont.)

  • Reflection of Elastic Waves from a Plane Boundary
  • Scattering of Monochromatic SH Waves
  • Diffraction of SH Wave by a Long Crack
  • Rayleigh Surface Waves

Problem set 3 due

Two Dimensional Waves (cont.)

  • Elastic Waves due to a Load Traveling on the Ground Surface
  • Partial Wave Expansion
  • Approximate Evaluation of an Integral

Mid-term quiz out

Waves in Water

  • Governing Equations for Waves on the Sea Surface
  • Progressive Waves on a Sea of Constant Depth
  • Wave Resistance of a Two-dimensional Obstacle

Mid-term quiz due

Waves in Water (cont.)

  • Narrow-banded Dispersive Waves in General
  • Radiation of Surface Waves Forced by an Oscillating Pressure
  • The Kelvin Pattern of Ship Wave

Problem set 4 out

Waves in Water (cont.)

  • Basic Theory for Two-dimensional Internal Waves in a Stratified Fluid
  • Internal Waves Modes for Finite N
  • Internal Waves in a Vertically Unbounded Fluid
  • Reflection of Internal Waves at Boundary

Problem set 4 due

Wave Localization

  • Wave Localization in a Random Medium
  • References

Problem set 5 out

Forced Dispersive Waves Along a Narrow Channel

  • Free Wave Propagation Along a Narrow Waveguide

Problem set 5 due

Forced Dispersive Waves Along a Narrow Channel (cont.)

  • Forced Wave Propagation Along a Narrow Waveguide
  • Initial Boundary Value Problem

Final quiz out

Internal Waves in a Stratified Fluid

  • Introduction
  • Governing Equations for Incompressible Density-stratified Fluid
  • The Buoyancy Frequency (Brunt-Vaisala Frequency)

Final quiz due

Internal Waves in a Stratified Fluid (cont.)

  • Internal Gravity Waves in Unbounded Stratified Fluid
  • Waveguide Behavior