General Propagation Direction A By Substitution In 57

General propagation direction 

(a) By substitution in (57) Ibid the determinantal equation which expresses the condition that the displacement R(r) = [u0x + v0y + w0z] exp [i(K∙ r – wt)] be a solution of the elastic wave equations in a cubic crystal. (b) The sum of the roots of a determinantal equation is equal to the sum of the diagonal elements aii Show from part (a) that the sum of the squares of the three elastic wave velocities in any direction in a cubic crystal is equal to (C11 + 2C44)/p. Recall that v2s, = w2/K2.

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