Solve Harmonic Wave Equation: Manish from Germany

[reedc15]

Dear Guys,

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

Manish
Germany

 

[mathman]

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]

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

 

[TheDragon]

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]

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]

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.