Impurity Phonon Mode* Consider a harmonic chain where all spring constants have the same value κand masses have value m, except for the mass at position n=0 which instead has value M<m as shown in this figure: Along with traveling wave solutions, there can be a standing wave normal mode localized near the impurity. Use an ansatz of the form δxn=A e^i ωt-q|n| α with q real to solve for the frequency of this impurity mode. Consider your result in the context of Exercise 9.4. | Numerade