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Waves and energy



On February 23  David Abineri wrote:

> If two electromagnetic waves interfere destructively, what happens to the 
> energy associated with the waves? I am guessing that on the large scale, 
> in a double slit experiment that additional energy shows up at the points 
> of constructive interference that compensates for the loss at the nodes. 
> But, what about looking as just the waves that are meeting at a node?

Let me rephrase this question to show a situation in which the answer is
not obvious to me. Suppose we have two parallel laser beams whose temporary
coherence is nearly PERFECT. The first beam travels along the x axis 
passing a beam splitter positioned at 45 degrees. The second beam, after 
being reflected from a mirror, and from the beam splitter, is superimposed 
on the first one. The phase relation between the beams can be controlled 
by a retarding glass wedge of variable thickness (from zero to lambda/4).
This will keep beams out of phase. The beams are polarized in the same plane.

In principle, this arrangement will create two electromagnetic waves which
are out of phase everywhere after the beam splitter. It will be a very long
"antinode". A wall perpendicular to the x axis should be able to display a 
bright spot for each individual beam but no for the combination of two beams. 
Can this be demonstrated? If so, I predict that the beam splitter will loose 
its semitransparancy. The first beam will be mostly reflected and the second 
beam would be mostly transmitted. Does this make any sens?

I suppose a similar situation can be created with sound waves (two phase-
correlated spekers at the entrence of a long pipe). The reflected sound 
can be suppressed, for example, by making the pipe very long. Will the 
pipe's entrence  become a strong reflector when two beams are "trying to 
enter" it at the same time?  

                                        Ludwik Kowalski