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| Q: | Light waves from two sources of light meet. They are in phase such that they cancel each other out. Is this an exception to the Conservation of Energy Law? If not, why not?
-Steve
Northfield MN |
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| A: |
Nice question!
If the waves canceled everywhere, that would indeed violate energy conservation. However, what happens is that for any actual wave patterns, there are regions of both constructive interference and destructive interference, so that net energy is exactly conserved.
For the slightly mathematicaly inclined, here’s an explanation. Take two wave pulses from two completely separate sources, a and b. Initially, the waves don’t overlap, so their dot product (meaning the integral over space of the dot products of their fields) is zero. The linear wave equation keeps that dot product constant. The energy depends on the square of the fields, e.g. (E_a)^2 + (E_b)^2 +2 (E_a*E_b). Although if the waves move so that they overlap the last term is not zero everywhere, its integral over space remains zero.
Mike W.
(republished on 07/28/06) |
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