Homework # 4 (due Thursday, 10 February) 1. Consider a longitudinal wave ( 29 cos ϖ =-n u A qna t in a monoatomic linear lattice of atoms of mass M , spacing a and nearest-neighbor interaction C . (a) Show that the total energy of the wave is given by ( 29 2 2 1 1 1 2 2 + ± = +-² ³ ´ µ ¶ ¶ n n n n n du E M C u u dt , where n runs over all atoms. (b) Show that the time-averaged kinetic energy is equal to the time-averaged potential energy. (c) Show that the total time-averaged energy per atom is equal to ½ MA 2 2 . 2. Consider a linear chain in which alternative ions have masses M 1 and M 2 and only nearest neighbors interact. (a) Discuss the form of the dispersion relation and the nature of the vibrational
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This note was uploaded on 09/21/2011 for the course PHYSICS 101 taught by Professor Wormer during the Spring '08 term at Aarhus Universitet.