Harmonic Wave Equation

  • Thread starter reedc15
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  • #1
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Dear Guys,

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

Manish
Germany
 

Answers and Replies

  • #2
mathman
Science Advisor
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Dear Guys,

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

Manish
Germany
Yes. Separate the real (cosine) and imaginary parts (sine).
 
  • #3
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Ok, but what about the quadratic exponent? Would my wave equation still be harmonic?
 
  • #4
10
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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.
 
  • #5
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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)
 
  • #6
10
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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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