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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

PHY 7 11 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 Brief review of 1-d from Chap. 7 Waves in 2-d elastic membranes – Chap. 8.

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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

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  1. 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 • Brief review of 1-d from Chap. 7 • Waves in 2-d elastic membranes – Chap. 8 PHY 711 Fall 2013 -- Lecture 26

  2. PHY 711 Fall 2013 -- Lecture 26

  3. Review of wave equation in one-dimension – here m(x,t) can describe either a longitudinal or transverse wave. Traveling wave solutions -- PHY 711 Fall 2013 -- Lecture 26

  4. PHY 711 Fall 2013 -- Lecture 26

  5. Standing wave solutions of wave equation: PHY 711 Fall 2013 -- Lecture 26

  6. PHY 711 Fall 2013 -- Lecture 26

  7. Extension of ideas to wave motion on a two-dimensional surface – elastic membrane (transverse wave; linear regime). u(x,y,t) PHY 711 Fall 2013 -- Lecture 26

  8. PHY 711 Fall 2013 -- Lecture 26

  9. PHY 711 Fall 2013 -- Lecture 26

  10. Consider a rectangular boundary: a b PHY 711 Fall 2013 -- Lecture 26

  11. PHY 711 Fall 2013 -- Lecture 26

  12. More general boundary conditions: PHY 711 Fall 2013 -- Lecture 26

  13. Consider a circular boundary: R PHY 711 Fall 2013 -- Lecture 26

  14. Consider circular boundary -- continued PHY 711 Fall 2013 -- Lecture 26

  15. Some properties of Bessel functions PHY 711 Fall 2013 -- Lecture 26

  16. Some properties of Bessel functions -- continued PHY 711 Fall 2013 -- Lecture 26

  17. PHY 711 Fall 2013 -- Lecture 26

  18. PHY 711 Fall 2013 -- Lecture 26

  19. 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 PHY 711 Fall 2013 -- Lecture 26

  20. Introduction to algebraic manipulation software Available from the webpage: http://help.wfu.edu/public/vcl If you have any trouble with this installation and setup, please contact Ching-Wan Yip at yipcw@wfu.edu 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. PHY 711 Fall 2013 -- Lecture 26

  21. PHY 711 Fall 2013 -- Lecture 26

  22. PHY 711 Fall 2013 -- Lecture 26

  23. PHY 711 Fall 2013 -- Lecture 26

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