Previous:
Types of Waves
Elastostatics (when the body is governed by Laplace equation) is governed by elliptic partial differential equations. However, when the same body is loaded dynamically, then the governing equation becomes hyperbolic. While the former is specified by boundary conditions, the latter is prescribed by boundary and initial conditions.
Consider the particle displacement
Note
that the motion along
direction and the wave (phase) velocity is
in the +ve
direction. l is the wavelength.
Particle velocity at a given
Strain
Stress
In the absence of body forces, equation of equilibrium is
Substituting
and using
, we have
Thus
the longitudinal wave travels at a velocity of
and is only a function of
(elastic constants) and density.
Next: 5.8 (b) Plane Irrotational Waves
11/29/01 0:42:33