Question

Derive an expression for the velocity of the transverse wave in the [100] direction

in a cubic crystal.

Answer 1

Consider a transverse or shear wave with the wavevector along the 𝑥 cube edge and with the particle displacement 𝑣 in the 𝑦 direction:

$$v=v_0e^{i(kx-\omega t)}$$

The  dispersion relation

$$\rho \omega^2=C_{11}K^2$$

thus the velocity of a transverse wave in the [100] direction is

$$v_s=\frac{C_{11}^2}{\rho^2}$$