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*From*: John Denker <jsd@AV8N.COM>*Date*: Mon, 9 Feb 2004 13:48:03 -0800

Quoting Ludwik Kowalski <kowalskil@MAIL.MONTCLAIR.EDU>:

The power formula in a textbook is derived

by integrating kinetic energy along one

lambda and then potential energy along one

lambda. The two are added and the sum is

divided by the period T. This gives

P=0.5*mu*w^2*A^2*v [1]

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 [1] make some

sense in the context of a running wave. They make no sense

whatsoever in the context of a standing wave.

The formula contains no parameters representing dissipation,

so it cannot describe a dissipative situation. In the

absence of dissipation, a standing wave requires ZERO

power, so the formula overestimates the power by a factor

of infinity.

In more detail: the formula [1] is off by a factor of Q,

roughly speaking. The formula tells you how much power you

put into the running wave, while Q tells you how many copies

of the running wave get reflected back to make the standing

wave you observe.

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