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

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

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- 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

- Wave equation for sound

PHY 711 Fall 2012 -- Lecture 32

Other solutions to wave equation:

PHY 711 Fall 2012 -- Lecture 32

PHY 711 Fall 2012 -- Lecture 32

Wave equation with source -- continued:

PHY 711 Fall 2012 -- Lecture 32

Derivation of Green’s function for wave equation

PHY 711 Fall 2012 -- Lecture 32

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

PHY 711 Fall 2012 -- Lecture 32

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

PHY 711 Fall 2012 -- Lecture 32

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

PHY 711 Fall 2012 -- Lecture 32

Derivation of Green’s function for wave equation – continued

need to find A and B.

PHY 711 Fall 2012 -- Lecture 32

Derivation of Green’s function for wave equation – continued

PHY 711 Fall 2012 -- Lecture 32

Derivation of Green’s function for wave equation – continued

PHY 711 Fall 2012 -- Lecture 32

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 711 Fall 2012 -- Lecture 32 Green’s function:

PHY 711 Fall 2012 -- Lecture 32 Green’s function:

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