# Show that the second moment (overline{I^{2}}) of the intensity of a wave is not equal to the

## Question:

Show that the second moment \(\overline{I^{2}}\) of the intensity of a wave is not equal to the fourth moment \(\overline{\left[u^{(r)}\right]^{4}}\) of the real amplitude of that wave, the difference being due to a low-pass filtering operation and a scaling by a factor of 2 implicit in the definition of intensity.

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