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Finding Two Wave's Common Amplitude

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data
    Two sinusoidal waves, identical except for phase, travel in the same direction along a string producing a net wave y'(x, t) = (1.0 mm) sin(18x - 4.0t + 0.960 rad), with x in meters and t in seconds.

    (a) What is the wavelength λ of the two waves?
    (b) What is the phase difference between them?
    (c) What is their amplitude ym?

    I got A and B correct with answers of 0.35 and 1.92

    2. Relevant equations
    y'm = 2ym cos([tex]\frac{\Phi}{2}[/tex])


    3. The attempt at a solution

    I set y'm = 1 mm and [tex]\frac{\Phi}{2}[/tex] = 0.96

    Then

    [tex]\frac{1}{2cos(.96)}[/tex] = ym

    0.5 = ym (Rounding)

    Not sure what I'm doing wrong.

    Any help is appreciated.

    Thanks!
     
    Last edited: Nov 19, 2009
  2. jcsd
  3. Nov 19, 2009 #2
    I found my answer. I took the given equation and set it equal to the sum equation.

    I then set x and t to zero and solved for ym

    That led to

    [tex]\frac{sin(\frac{\Phi}{2})}{sin(\Phi)}[/tex]

    In this case


    [tex]\frac{sin(.96)}{sin(1.92)}[/tex] = ym = .872
     
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