All Problems

Elastic Waves. Acoustics.

Problem 4.151

A plane harmonic wave with frequency \(\omega\) propagates at a velocity \(v\) in a direction forming angles \(\alpha, \beta, \gamma\) with the \(x, y, z\) axes. Find the phase difference between the oscillations at the points of medium with coordinates \(x_{1}, y_{1}, z_{1}\) and \(x_{2}, y_{2}, z_{2}\)

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|