# Harmonic Wave Equation

by reedc15
Tags: equation, harmonic, wave
P: 5,776
Yes. Separate the real (cosine) and imaginary parts (sine).
 P: 8 Ok, but what about the quadratic exponent? Would my wave equation still be harmonic?
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.
 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)
 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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