4.9 Consider a longitudinal wave Sn So cos (@t- nka) = which propagates in a monatomic linear lattice of atoms of mass M

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4 9 Consider A Longitudinal Wave Sn So Cos T Nka Which Propagates In A Monatomic Linear Lattice Of Atoms Of Mass M 1 (34.06 KiB) Viewed 47 times

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4.9 Consider a longitudinal wave Sn So cos (@t- nka) = which propagates in a monatomic linear lattice of atoms of mass M, spacing a and the force constant f. (a) Show that the total energy of the wave is dsn E = 1/2 M ² (dha) + 1/2 (s. - 5+1)³² Σ dt where n runs over all atoms. (b) By substituting s, in this expression and using the dispersion relation (4.4), show that the time-average total energy per atom is 1 - Mw³s +1/ƒ(1 − cos ka) s² = — - Mw²s² 4