Harmonic Wave Equation


by reedc15
Tags: equation, harmonic, wave
reedc15
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#1
Feb16-13, 03:26 PM
P: 8
Dear Guys,

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

Manish
Germany
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mathman
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#2
Feb16-13, 03:30 PM
Sci Advisor
P: 5,935
Quote Quote by reedc15 View Post
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).
reedc15
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#3
Feb17-13, 10:04 AM
P: 8
Ok, but what about the quadratic exponent? Would my wave equation still be harmonic?

TheDragon
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#4
Feb17-13, 11:52 AM
P: 10

Harmonic Wave Equation


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.
reedc15
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#5
Feb17-13, 12:07 PM
P: 8
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)
TheDragon
TheDragon is offline
#6
Feb18-13, 03:52 AM
P: 10
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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