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Homework Help: Determining total amplitude of out of phase waves

  1. Oct 4, 2004 #1

    Gza

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    I understand there is a way to solve the problem with complex numbers, but am at a loss as to how:

    Determine the amplitude of the resultant motion when two sinusoidal motions having the same frequency and traveling in the same direction are combined, if their amplitudes are 3 cm and 4 cm and they differ in phase by pi/2 radians.
     
  2. jcsd
  3. Oct 4, 2004 #2

    Tide

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    The amplitude will be 5!

    Basically

    [tex]A = 3 \sin X + 4 \cos X = 5 \left ( \frac {3}{5} \sin X + \frac {4}{5} \cos X \right)[/tex]

    where X is the time/space phase. Now just define [itex]\phi = \tan^{-1} \frac {4}{3}[/itex] so that

    [tex]A = 5 \sin \left( X+\phi \right)[/tex]
     
  4. Oct 6, 2004 #3

    Gza

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    You are a busy man tide! Thanks for the help. :smile:
     
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