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> P=0.5*mu*w^2*A^2*v 
This is an object lesson in the perils of plug-and-chug,
or to say the same thing in more positive terms, a lesson
in the importance of knowing the domain of applicability
and validity of a formula.
That derivation and the resulting formula  make some
sense in the context of a running wave. They make no sense
whatsoever in the context of a standing wave.