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Old April 21st 07, 03:03 PM posted to rec.radio.amateur.antenna
Dave Dave is offline
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First recorded activity by RadioBanter: Jul 2006
Posts: 797
Default Independence of waves


"Cecil Moore" wrote in message
...
Dave wrote:
Now the big question is: Is superposition always reversible?
If not, it implies interaction between f(x) and f(y).


as long as everything is linear, yes.


This is really interesting. Given the following:

b1 = s11(a1) + s12(a2) = 0

Let P1 = |s11(a1)|^2 = 1 joule/sec

Let P2 = |s12(a2)|^2 = 1 joule/sec

Therefore, Ptot = |b1|^2 = 0 joules/sec

Ptot = P1 + P2 + 2*SQRT(P1*P2)cos(180)

Ptot = 1 + 1 - 2 = 0 joules/sec = |b1|^2

Can one reverse the superposition whose result is
zero to recover the original two component waves?
If not, isn't that proof that the two original
component waves interacted?
--
73, Cecil http://www.w5dxp.com


no, because you have done a non-linear operation on them by converting to
powers. obviously at the start 'a1' and 'a2' are separate.