Velocity Waves at a Rigid Termination

Since the displacement is always zero at a rigid termination, the velocity is also zero there:

$\displaystyle v(t,0) \equiv 0 \qquad v(t,L) \equiv 0$

Therefore, velocity waves reflect from a rigid termination with a sign flip, just like displacement waves:

$\displaystyle v^{+}(n)$	$\displaystyle =$	$\displaystyle -v^{-}(n)$
$\displaystyle v^{-}(n+N/2)$	$\displaystyle =$	$\displaystyle -v^{+}(n-N/2) \protect$	(7.12)

Such inverting reflections for velocity waves at a rigid termination are identical for models of vibrating strings and acoustic tubes.