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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 Plan for Lecture 18: Finish reading Chapter 4 and start reading Chapter 7 Coupled motion for extended systems; relationship to continuum models Wave equation. Lattice vibrations for 3-dimensional lattice.

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PHY 711 Classical Mechanics and Mathematical Methods

  • 10-10:50 AM MWF Olin 103
  • Plan for Lecture 18:
      • Finish reading Chapter 4 and start reading Chapter 7
        • Coupled motion for extended systems; relationship to continuum models
        • Wave equation

PHY 711 Fall 2012 -- Lecture 18

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Lattice vibrations for 3-dimensional lattice

Example: diamond lattice

Ref: http://phycomp.technion.ac.il/~nika/diamond_structure.html

PHY 711 Fall 2012 -- Lecture 18

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B. P. Pandy and B. Dayal, J. Phys. C. Solid State Phys. 6 2943 (1973)

Note: Longitudinal, transverse, and combination modes occur.

PHY 711 Fall 2012 -- Lecture 18

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Longitudinal versus transverse vibrations

Images from web page:

http://www.physicsclassroom.com/class/waves/u10l1c.cfm

PHY 711 Fall 2012 -- Lecture 18

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Longitudinal case: a system of masses and springs:

m

m

m

PHY 711 Fall 2012 -- Lecture 18

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system parameter with units of (velocity)2

PHY 711 Fall 2012 -- Lecture 18

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t

Transverse displacement:

m(x,t)

PHY 711 Fall 2012 -- Lecture 18