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Basic Phasor addition

  1. Oct 3, 2011 #1
    1. The problem statement, all variables and given/known data

    If I have three different waves each with difference amplitude and phase angle how would i find the combined phase angle shift?

    wave 1: A=5 phi=0
    wave 2: A=5 phi=pi/4
    wave 3: A=9 phi=pi/2

    2. Relevant equations

    phi'=arctan(a2sin(phi)/(a1+a2cos(phi)), where phi in this case is the difference between the phase angles of two waves.

    3. The attempt at a solution

    My first strategy was to add wave 1 and 2 and then add their sum to wave three. this gave me the correct combined amplitude of 15.29. I then applied the same thinking to the phase angles but the answer i got was incorrect so i tried vector addition and using the law of cosines and I got a nonsensical answer - arcos(-1.41). Needless to say i need a nudge in the right direction. Thanks for the help
     
  2. jcsd
  3. Oct 3, 2011 #2

    Redbelly98

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    Think of the (A,Φ) values as polar coordinates of vectors. Convert them to (x,y) coordinates, and then it's standard vector addition from there.
     
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