Problem 4.157

A plane elastic wave \(\xi=a e^{-\gamma x} \cos (\omega t-k x),\) where \(a, \gamma,\) \(\omega,\) and \(k\) are constants, propagates in a homogeneous medium. Find the phase difference between the oscillations at the points where the particles' displacement amplitudes differ by \(\eta=1.0 \%,\) if \(\gamma=\) \(=0.42 \mathrm{~m}^{-1}\) and the wavelength is \(\lambda=50 \mathrm{~cm}\)