1

Sample Wave Problems
 Transverse Vibration of a Taut String
 Longitudinal Vibration of an Elastic Rod
 Traffic Flow on a Freeway

Problem set 1 out

2

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

3

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

4

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

5

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

6

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

7

Two Dimensional Waves (cont.)
 Elastic Waves due to a Load Traveling on the Ground Surface
 Partial Wave Expansion
 Approximate Evaluation of an Integral

Midterm quiz out

8

Waves in Water
 Governing Equations for Waves on the Sea Surface
 Progressive Waves on a Sea of Constant Depth
 Wave Resistance of a Twodimensional Obstacle

Midterm quiz due

9

Waves in Water (cont.)
 Narrowbanded Dispersive Waves in General
 Radiation of Surface Waves Forced by an Oscillating Pressure
 The Kelvin Pattern of Ship Wave

Problem set 4 out

10

Waves in Water (cont.)
 Basic Theory for Twodimensional 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

11

Wave Localization
 Wave Localization in a Random Medium
 References

Problem set 5 out

12

Forced Dispersive Waves Along a Narrow Channel
 Free Wave Propagation Along a Narrow Waveguide

Problem set 5 due

13

Forced Dispersive Waves Along a Narrow Channel (cont.)
 Forced Wave Propagation Along a Narrow Waveguide
 Initial Boundary Value Problem

Final quiz out

14

Internal Waves in a Stratified Fluid
 Introduction
 Governing Equations for Incompressible Densitystratified Fluid
 The Buoyancy Frequency (BruntVaisala Frequency)

Final quiz due

15

Internal Waves in a Stratified Fluid (cont.)
 Internal Gravity Waves in Unbounded Stratified Fluid
 Waveguide Behavior

