The dispersion relation of a monatomic chain is described by the relation |sin-ka| 4C where w...

 

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The dispersion relation of a monatomic chain is described by the relation |sin-ka| 4C where w is the frequency, k is the wavevector, a is the spacing between the atoms, C is the spring constant of the bond between the atoms and m is the mass of the atoms. What is the maximum frequency that can propagate along the chain? Over what range is this function fully defined, and what important feature of reciprocal space does this range delineate? [ The dispersion relation of a monatomic chain is described by the relation |sin-ka| 4C where w is the frequency, k is the wavevector, a is the spacing between the atoms, C is the spring constant of the bond between the atoms and m is the mass of the atoms. What is the maximum frequency that can propagate along the chain? Over what range is this function fully defined, and what important feature of reciprocal space does this range delineate? [