Lecture Notes


Chapter 1: Sample Wave Problems

Transverse Vibration of a Taut String

Longitudinal Vibration of an Elastic Rod

Traffic Flow on a Freeway

Wave Propagation in Arteries

Shallow Water Waves and Linearization

Sound in Fluids

Flexural Waves in a Beam on an Elastic Foundation


Chapter 2: One Dimensional Waves

General Solution to Wave Equation

Branching of Arteries

Waves in an Infinite Domain due to Initial Disturbances

Reflection of Shallow Water Waves from a Cliff

Forced Waves in an Infinite Domain

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


Chapter 3: 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

Reflection of Elastic Waves from a Plane Boundary

Scattering of Monochromatic SH Waves

Diffraction of SH Wave by a Long Crack

Rayleigh Surface Waves

Elastic Waves due to a Load Traveling on the Ground Surface

Partial Wave Expansion

Approximate Evaluation of an Integral


Chapter 4: 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

Narrow-banded Dispersive Waves in General

Radiation of Surface Waves Forced by an Oscillating Pressure

The Kelvin Pattern of Ship Wave

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


Chapter 5: Miscellaneous Topic

Wave Localization in a Random Medium



Chapter 6: Forced Dispersive Waves Along a Narrow Channel

Free Wave Propagation Along a Narrow Waveguide

Forced Wave Propagation Along a Narrow Waveguide

Initial Boundary Value Problem


Chapter 7: Internal Waves in a Stratified Fluid


Governing Equations for Incompressible Density-stratified Fluid

The Buoyancy Frequency (Brunt-Vaisala Frequency)

Internal Gravity Waves in Unbounded Stratified Fluid

Waveguide Behavior