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Harmonic Wave Equation 
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#1
Feb1613, 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 


#2
Feb1613, 03:30 PM

Sci Advisor
P: 6,039




#3
Feb1713, 10:04 AM

P: 8

Ok, but what about the quadratic exponent? Would my wave equation still be harmonic?



#4
Feb1713, 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. 


#5
Feb1713, 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)



#6
Feb1813, 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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