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.