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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 C;is mo =c.a-cos(nka). For ka <«1, the speed of sound in this limit has form
4C, +C
2ka
m
C+2C,
2ka
m
2C+C ka
m
C+4C, ka

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