
469Shock Physics
We can then write Equation 16.206 as
net
xl
=
(16.214)
Thus at a rigid boundary, the stress is doubled while the displacement and particle veloci-
ties are zero.
These equations allow us to visualize wave interactions with xed or free ends as fol-
lows. When a tensile wave encounters a free boundary, it is reected as a compressive
wave. If we have a free surface, we can imagine a phantom pulse coming in from outside
the bar as depicted in Figure 16.27. With a xed boundary, the imagined pulse is in the
same sense as the incident pulse as depicted in Figure 16.28.
u,v
c
L
u,v
Free surface ...