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The dispersion relation for one dimensional lattice vibrations of chain of identical mass m, in
whach mass is connected to first and second nearest neighbors by coupling constants C:
and Cis me =C,(a-cos(nka). For ka c«1, the speed of sound in this limit has fom
4C,+C ka
C+2C,
ka
m
2C, +C, ka
C+4C, ka
m

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