Axial impact on a deformable body results in a disturbance which initially propagates away from the impact site at a specific speed. This disturbance is a pulse or wave of particle displacement (and consequent stress). Wave propagation relates to propagation of a coherent pulse of stress and particle displacement through a medium at a finite speed. Familiar manifestations of this phenomenon are the transmission of sound through air, water waves across the surface of the sea and seismic tremors through the earth; thus, waves exist in gases, liquids and solids. Sources of excitation may be either concentrated or distributed spatially, and brief or extended functions of time. The unifying characteristic of waves is propagation of a disturbance through a medium. Properties of the medium that result in waves and determine the speeds of propagation are the density ρ and moduli of deformability (Young's modulus E, shear modulus G, bulk modulus K, etc.).

Longitudinal Wave in Uniform Elastic Bar

Consider a uniform slender elastic bar of cross-sectional are A, elastic modulus E and density ρ; the bar contains a region with axial stress σ(x, t) that is propagating in the positive x direction as shown in Fig. 7.1.