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


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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 32: Wave equation for sound Green’s function for wave equation. Other solutions to wave equation:. Wave equation with source:. Wave equation with source -- continued:.

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

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Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

  • PHY 711 Classical Mechanics and Mathematical Methods

  • 10-10:50 AM MWF Olin 103

  • Plan for Lecture 32:

    • Wave equation for sound

      • Green’s function for wave equation

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

Other solutions to wave equation:

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

Wave equation with source:

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

Wave equation with source -- continued:

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

Derivation of Green’s function for wave equation

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

Derivation of Green’s function for wave equation -- continued

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

Derivation of Green’s function for wave equation -- continued

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

Derivation of Green’s function for wave equation -- continued

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

Derivation of Green’s function for wave equation – continued

need to find A and B.

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

Derivation of Green’s function for wave equation – continued

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

Derivation of Green’s function for wave equation – continued

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

For time harmonic forcing term we can use the corresponding Green’s function:

In fact, this Green’s function is appropriate for boundary conditions at infinity. For surface boundary conditions where we know the boundary values or their gradients, the Green’s function must be modified.

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

PHY 711 Fall 2012 -- Lecture 32


Phy 7 11 classical mechanics and mathematical methods 10 10 50 am mwf olin 103

PHY 711 Fall 2012 -- Lecture 32


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