
#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: 5,935





#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. 


Register to reply 
Related Discussions  
Expressions of travelling harmonic wave equation  Introductory Physics Homework  5  
harmonic wave equation  Classical Physics  6  
Show that a wave function fits the Schrödinger's equation. (Harmonic oscillator)  Advanced Physics Homework  7  
What Is Schrodigner Wave Equation & Its App. To One Dimensional Harmonic Oscillator?  Quantum Physics  3  
two particles in a potential (wave equation and harmonic oscillators)  Advanced Physics Homework  1 