Results 1 to 2 of 2

Thread: Riddle # 132 (Solved)

  1. #1
    Join Date
    Feb 2008
    Location
    Karachi, Pakistan, Pakistan
    Posts
    125,914
    Mentioned
    839 Post(s)
    Tagged
    9270 Thread(s)
    Thanked
    1181
    Rep Power
    21474971

    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
    صرف آواز نہیں ، لفظ بھی مقفل ہیں مرے

    سوچ میں ہوں کہ اب تجھ کو پکاروں کیسے

  2. #2
    Join Date
    Feb 2008
    Location
    Karachi, Pakistan, Pakistan
    Posts
    125,914
    Mentioned
    839 Post(s)
    Tagged
    9270 Thread(s)
    Thanked
    1181
    Rep Power
    21474971

    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.
    صرف آواز نہیں ، لفظ بھی مقفل ہیں مرے

    سوچ میں ہوں کہ اب تجھ کو پکاروں کیسے

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •