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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 31: Wave equation for sound Standing waves Green’s function for wave equation; wave scattering. Linearization of the fluid dynamics relations:. Time harmonic standing waves in a pipe. a. L.

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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 31: • Wave equation for sound • Standing waves • Green’s function for wave equation; wave scattering PHY 711 Fall 2012 -- Lecture 31

  2. PHY 711 Fall 2012 -- Lecture 31

  3. Linearization of the fluid dynamics relations: PHY 711 Fall 2012 -- Lecture 31

  4. PHY 711 Fall 2012 -- Lecture 31

  5. PHY 711 Fall 2012 -- Lecture 31

  6. Time harmonic standing waves in a pipe a L PHY 711 Fall 2012 -- Lecture 31

  7. PHY 711 Fall 2012 -- Lecture 31

  8. PHY 711 Fall 2012 -- Lecture 31

  9. PHY 711 Fall 2012 -- Lecture 31

  10. m=0 m=1 m=2 PHY 711 Fall 2012 -- Lecture 31

  11. m=1 m=2 m=0 Zeros of derivatives: m=0: 0.00000, 3.83171, 7.01559 m=1: 1.84118, 5.33144, 8.53632 m=2: 3.05424, 6.70613, 9.96947 PHY 711 Fall 2012 -- Lecture 31

  12. Boundary condition for z=0, z=L: PHY 711 Fall 2012 -- Lecture 31

  13. Example PHY 711 Fall 2012 -- Lecture 31

  14. Alternate boundary condition for z=0, z=L: PHY 711 Fall 2012 -- Lecture 31

  15. Other solutions to wave equation: PHY 711 Fall 2012 -- Lecture 31

  16. Wave equation with source: PHY 711 Fall 2012 -- Lecture 31

  17. Wave equation with source -- continued: PHY 711 Fall 2012 -- Lecture 31

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