11/04/2013PHY 711 Fall 2013 -- Lecture 261 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 26: Traveling.

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PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
WHAT IS A WAVE? disturbance that transports energy through matter or space.
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
Electromagnetic waves due to specific sources
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
Presentation transcript:

11/04/2013PHY 711 Fall Lecture 261 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 26: Traveling and standing waves in 1 and 2 dimensions 1.Brief review of 1-d from Chap. 7 2.Waves in 2-d elastic membranes – Chap. 8

11/04/2013PHY 711 Fall Lecture 262

11/04/2013PHY 711 Fall Lecture 263 Review of wave equation in one-dimension – here  (x,t) can describe either a longitudinal or transverse wave. Traveling wave solutions --

11/04/2013PHY 711 Fall Lecture 264

11/04/2013PHY 711 Fall Lecture 265 Standing wave solutions of wave equation:

11/04/2013PHY 711 Fall Lecture 266

11/04/2013PHY 711 Fall Lecture 267 Extension of ideas to wave motion on a two-dimensional surface – elastic membrane (transverse wave; linear regime). u(x,y,t)

11/04/2013PHY 711 Fall Lecture 268

11/04/2013PHY 711 Fall Lecture 269

11/04/2013PHY 711 Fall Lecture 2610 Consider a rectangular boundary: a b

11/04/2013PHY 711 Fall Lecture 2611

11/04/2013PHY 711 Fall Lecture 2612 More general boundary conditions:

11/04/2013PHY 711 Fall Lecture 2613 Consider a circular boundary: R

11/04/2013PHY 711 Fall Lecture 2614 Consider circular boundary -- continued

11/04/2013PHY 711 Fall Lecture 2615 Some properties of Bessel functions

11/04/2013PHY 711 Fall Lecture 2616 Some properties of Bessel functions -- continued

11/04/2013PHY 711 Fall Lecture 2617

11/04/2013PHY 711 Fall Lecture 2618

11/04/2013PHY 711 Fall Lecture 2619 Maple server evaluation project  Request from Rick Matthews, Associate Provost for Technology and Information Systems  The University is exploring the possibility of making Maple available on a server rather than on individual computers  Need students to exercise the software  Need students to assess the performanc  Need students to identify issues  Entirely voluntary Possible pizza party or ??? rewards

11/04/2013PHY 711 Fall Lecture 2620 Introduction to algebraic manipulation software Available from the webpage: If you have any trouble with this installation and setup, please contact Ching-Wan Yip at Note: This is a remote server that the university is testing. If you are off campus you will need to use VPN to gain access.

11/04/2013PHY 711 Fall Lecture 2621

11/04/2013PHY 711 Fall Lecture 2622

11/04/2013PHY 711 Fall Lecture 2623

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