Problem 4.156

A plane wave \(\xi=a \cos (\omega t-k x)\) propagates in a homogeneous elastic medium. For the moment \(t=0\) draw (a) the plots of \(\xi, \partial \xi / \partial t,\) and \(\partial \xi / \partial x\) vs \(x\); (b) the velocity direction of the particles of the medium at the points where \(\xi=0,\) for the cases of longitudinal and transverse waves; (c) the approximate plot of density distribution \(\rho(x)\) of the medium for the case of longitudinal waves.