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The fields sum, but the intensity of the sum isn't the same as the sum of the intensities.

This simple example may help:
2^2 + 3^2 = 4 + 9 = 15.
(2 + 3)^2 = 5^2 = 25.

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Q: Why is the resultant intensity not the sum of intensities due to separate disturbances?
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