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Thread: Riddle # 132 (Solved)

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    grin Riddle # 132 (Solved)

    What phase difference between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 1.45 times that of the common amplitude of the two combining waves? Express your answer in degrees, radians, and wavelengths.
    1) _____
    2) _____ rad
    3) _____ λ
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    Default Re: Riddle # 132

    Answer:

    This solution is based on the observation that two sinewaves of equal amplitude but differing phase have a maximum absolute sum where they intersect; this is shown by the fact that their slopes are equal in terms of |dy/dx| at the intersection, and as you move away, the decreasing function has a steeper slope than the increasing one. Any time that happens, you have a maximum sum.

    So we can say in this case that each amplitude = 0.725A. Then half the phase difference Δθ/2 = arccos(0.725) = 0.759762 rad; Δθ = 1.5195 rad = 87.06 deg = 0.2418λ.
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