Describe constructive and destructive interference in terms of the combining of crests and troughs and the reesulting amplitude.

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  1. T in degrees
    add A= sin wt + sin (wt + T)

    if T = 0
    A = 2 sin wt

    if T = 90
    A = sin wt + sin (wt+90)
    = 2 sin .5(2 wt +90) cos .5(-90)
    = 2 sin (wt + 45) cos 45
    = 2 (.707) sin (wt+45)
    phase changed, amplitude .707 times the constructive 2 A but still sqrt 2 or 1.41 times just one A

    If T = 180
    A = sin wt + sin (wt + 180)
    = 2 sin .5(2 wt +180) cos .5(-180)
    = 2 sin (wt + 90) cos 90
    but cos 90 = 0, result is nothing, destructive.

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  2. In other words, when the phase angle is zero, the crests add to give 2 A
    and when the crest is 180 degrees off, the trough lines up with a crest and gives zero.
    in between is in between.

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