Is it possible that phase reversals in a standing wave can occur via this mechanism? Consider the spatio-temporal standing wave as specified by

$f(x,t) = sin(\omega t) sin(k x)$

The zero'd boundary conditions are determined by setting the wave number k to $2\pi/L$ , which means that both $2\pi/L$ and $-2\pi/L$ are valid and so the sign of f(x,t) can conceivably change with a forcing perturbation localized in space.