Let's take two waves "y_1 \\ and \\ y_2" and are superposed
"y_1\n = a cos \u03c9t"
"y_2\n = a cos (\u03c9t + \u03c6 )"
and the resultant displacement will be given by
"y = y_1 + y_2"
"y= a [cos \u03c9t + cos (\u03c9t +\u03c6)]"
"y= 2 a cos (\u03c6\/2) cos (\u03c9t + \u03c6\/2)"
The amplitude of the resultant displacement is 2acos(φ/2) and therefore the intensity at that point will be
"I = 4 I_0\n cos^2\n (\u03c6\/2)"
If φ = 0, ± 2 π, ± 4 π,… we will have constructive interference leading to maximum intensity
If φ = ± π, ± 3π, ± 5π …we will have destructive interference leading to minimum intensity
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