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Elastic Waves. Acoustics.

Problem 4.151

A plane harmonic wave with frequency ω\omega propagates at a velocity vv in a direction forming angles α,β,γ\alpha, \beta, \gamma with the x,y,zx, y, z axes. Find the phase difference between the oscillations at the points of medium with coordinates x1,y1,z1x_{1}, y_{1}, z_{1} and x2,y2,z2x_{2}, y_{2}, z_{2}

Reveal Answer
Δφ=ωv∣(x1−x2)cos⁡α+(y1−y2)cos⁡β+(z1−z2)cos⁡γ∣\Delta \varphi=\frac{\omega}{v}\left|\left(x_{1}-x_{2}\right) \cos \alpha+\left(y_{1}-y_{2}\right) \cos \beta+\left(z_{1}-z_{2}\right) \cos \gamma\right|
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