Consider a one-dimensional chain of identical atoms. The springsbetween them alternate in strength between values K1 and K2.
a) Find the vibrational frequencies as a function of wave numberq. Study the low q limit and find the sound velocity.
b) Discuss the physical meaning of the two branches. Sketch theway the atoms move in both cases!
c) Discuss the dispersion and the normal modes for K1 ≫ K2.
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