Solve Harmonic Wave Equation: Manish from Germany

In summary, the conversation discusses whether the function f(x,t)=exp[-i(ax+bt)^2] qualifies as a harmonic wave. The group agrees that the function is not harmonic because it does not fulfill the requirement of f''=A*f when A is a constant. The quadratic exponent also does not meet the requirement.
  • #1
reedc15
8
0
Dear Guys,

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

Manish
Germany
 
Physics news on Phys.org
  • #2
reedc15 said:
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).
 
  • #3
Ok, but what about the quadratic exponent? Would my wave equation still be harmonic?
 
  • #4
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
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
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.
 

1. What is the harmonic wave equation?

The harmonic wave equation is a mathematical equation that describes the behavior of waves in a medium. It is a second-order partial differential equation that relates the second derivative of the wave function to its spatial and temporal derivatives.

2. How is the harmonic wave equation solved?

The harmonic wave equation can be solved using various methods, such as separation of variables, Fourier series, and Laplace transforms. The method used depends on the specific boundary conditions and initial conditions of the problem.

3. What is the significance of solving the harmonic wave equation?

Solving the harmonic wave equation allows us to understand and predict the behavior of waves in different mediums. This is crucial in many scientific fields, including acoustics, optics, and electromagnetism.

4. What are the applications of the harmonic wave equation?

The harmonic wave equation has numerous applications in physics and engineering. It is used to study sound and light waves, as well as to design and analyze electronic circuits and communication systems.

5. How does Manish from Germany relate to the harmonic wave equation?

Manish from Germany is likely a scientist or student who is interested in studying the harmonic wave equation and its applications. They may be conducting research or working on a project that involves solving this equation.

Similar threads

  • Introductory Physics Homework Help
Replies
9
Views
4K
  • Other Physics Topics
Replies
14
Views
2K
  • Other Physics Topics
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
831
  • Other Physics Topics
Replies
5
Views
9K
Replies
9
Views
723
  • Other Physics Topics
Replies
6
Views
1K
Replies
7
Views
2K
Replies
11
Views
774
Replies
1
Views
484
Back
Top