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Two waves in same direction

  1. Jan 26, 2008 #1
    1. The problem statement, all variables and given/known data

    Two waves travelling in the same direction are identical except for a phase difference. Show that if the amplitude of the sum of the waves is 1.5 times larger than the amplitude of the individual waves, then the phase difference must be

    delta(phi) = 2 arccos (3/4)
     
  2. jcsd
  3. Jan 27, 2008 #2

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    Let y1 and y2 be the displacements at a certain point due to the two waves. If the phase diff is 'b', then,

    y1 = a*sin(wt),
    y2 = a*sin(wt + b).

    The rest is algebraic. (Hint: add the two eqns.)
     
  4. Jan 27, 2008 #3
    thanks!

    now i tried...

    a*sin(wt)+a*sin(wt+b) = 2sin(wt+b/2)cos(b/2)

    substituted 1.5a for 2cos(b/2)

    a*sin(wt)+a*sin(wt+b) = (3/2)a*sin(wt+b/2)

    is this the right way to go? or maybe i just made some algebraic mistakes
     
  5. Jan 28, 2008 #4

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    Where is the 'a' on the RHS?

    ...for 2*a*cos(b/2)...OK?
     
  6. Jan 28, 2008 #5
    oh yes. thank you.
     
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