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Elastic Waves. Acoustics.

Problem 4.152

A plane wave of frequency \(\omega\) propagates so that a certain phase of oscillation moves along the \(x, y, z\) axes with velocities \(v_{1}\), \(v_{2}, v_{3}\) respectively. Find the wave vector \(\mathbf{k}\), assuming the unit vectors \(\mathrm{e}_ {x}, \mathrm{e}_ {y}, \mathrm{e}_ {z}\) of the coordinate axes to be assigned.

Reveal Answer
k=ω(exv1+eyv2+ezv3)\mathbf{k}=\omega\left(\frac{\mathbf{e}_{x}}{v_{1}}+\frac{\mathbf{e}_{y}}{v_{2}}+\frac{\mathbf{e}_{z}}{v_{3}}\right)
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