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Check 2 waave displacement equations please!

  1. Mar 22, 2012 #1
    Got to calculate the superposition of a couple o' waves, wanted to double check if they are both the same frequency and wavenumber?x1(t) = 3 sin(2t + /4 ) and x2(t) = 3 cos(2t).

    I take it 2 is the frequency? And since Kx is not inside the function how can I know whether the wave numbers the same? :S
     
  2. jcsd
  3. Mar 22, 2012 #2
    These are not waves. The equations have to spatial variable. They may represent two harmonic oscillations with a phase difference of pi/4.
    2∏ is the angular frequency, ω=2∏f. The frequency is 1 Hz.
     
  4. Mar 22, 2012 #3
    Ok thanks, when 2 harmonic oscillators superpose do you just take the sum of the two even though they have different phases?
    EDIT: Since one is in terms of sin and the other in cos, do i make sin(2pit+pi/4) into cos(2pit+pi/4+pi/2) or is that not valid, cuz i need to use the trig sum-product identity
     
    Last edited: Mar 22, 2012
  5. Mar 22, 2012 #4
    Yes, you add the functions. You don't need a trig sum-product identity. Use the phase identity sin(x) = cos(x-pi/2)
     
  6. Mar 22, 2012 #5
    Depends what you mean by the "take the sum".
    At any time, the total displacement is the sum of the two displacements (superposition principle):
    x(t)=x1(t)+x2(t)
    If you wish you can try to simplify or otherwise put the expression into a different form that shows something interesting.
    You cannot use the trig identity as the two have difefrent amplitudes.
    For the given case, you can write the result as a single cosine or sine,
    x(t)=Asin(2∏t+ψ).
    To find the values of A and ψ you can expand the sin and and identify the terms with the original components. You'll find two equations in the variables A and ψ.
    Phasor algebra is a more straightforward method, if you are familiar with it.
     
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