Write down the Christoffel wave equation for a wave in a cubic crystal propagating along the 111 direction For the choice C 11 1, C 12 C 44 0 5, and 1, use a program like Mathematica to find the eigenvectors of this matrix, which correspond to the polarizations of the propagating waves, and the vel...

Since the wave is propagating in the 111 direction all three k components are equal ie k3 thus kjkm ...

Write down the Christoffel wave equation for a wave in a cubic crystal propagating along the [111]

Question:

Write down the Christoffel wave equation for a wave in a cubic crystal propagating along the [111] direction. For the choice C₁₁ = 1, C₁₂ = C₄₄ = 0.5, and ρ = 1, use a program like Mathematica to find the eigenvectors of this matrix, which correspond to the polarizations of the propagating waves, and the velocity of each polarization.

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