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I think you pose an impossibility. Try to reduce it to practice, even
"gedankenly". How to manipulate two sources (or one split source) to
generate waves which cancel everywhere?
In this case we need to ask how you generated the waves.
There are various inequivalent possibilities, including:
1) Consider water waves...
2) Consider light waves with a beamsplitter...
axis
I arrange their phases so that the are exactly 180 deg out of phase.
... single frequency waves ... should
maintain their 180 deg phase difference at all points in space. I see no
way that they will interfere destructively along some portion of the x
and constructively along some other portion.