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Harmonic Wave Equation

  1. Feb 16, 2013 #1
    Dear Guys,

    Does f(x,t)=exp[-i(ax+bt)^2] qualify as a harmonic wave? Please help!

  2. jcsd
  3. Feb 16, 2013 #2


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    Science Advisor

    Yes. Separate the real (cosine) and imaginary parts (sine).
  4. Feb 17, 2013 #3
    Ok, but what about the quadratic exponent? Would my wave equation still be harmonic?
  5. Feb 17, 2013 #4
    i actually think not, cos(x^2) or cos(2x*t) is not an harmonic wave.
    in general, an harmonic function f is a function that gives f''=A*f when A is a constant. the function you gave do not fulfil this requirement.
  6. Feb 17, 2013 #5
    Yes, cos(x^2) is not a harmonic wave, but cos[(kx+wt)^2] is, I think. "f''=A*f when A is a constant" this requirement is also fulfilled, as f comes from w, and it will take integer multiple (given by constant A)
  7. Feb 18, 2013 #6
    I didn't understand what you mean,
    d^2 f/dx^2= -f*(2xk^2+2kwt)-2k^2*sin((kx+wt)^2)
    and nothing here suggest that there exist a constant A that for every t and every x
    d^2 f/dx^2=Af.
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