Problem 4.164

\(4.164 .\) The equation of a plane standing wave in a homogeneous elastic medium has the form \(\xi=a \cos k x \cdot \cos \omega t .\) Plot: (a) \(\xi\) and \(\partial \xi / \partial x\) as functions of \(x\) at the moments \(t=0\) and \(t=T / 2\), where \(T\) is the oscillation period; (b) the distribution of density \(\rho(x)\) of the medium at the moments \(t=0\) and \(t=T / 2\) in the case of longitudinal oscillations; (c) the velocity distribution of particles of the medium at the moment \(t=T / 4 ;\) indicate the directions of velocities at the antinodes, both for longitudinal and transverse oscillations.