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 a_ii 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 v²_s, = w²/K².