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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.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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