Can the Wave Equation Solution Use Only Positive Values of n?

In summary, the conversation discusses the correct way to write the general solution for an equation and whether it is acceptable to only use positive values of n in the solution. The speaker mentions that in their textbook, the result from a superposition is often written with only positive values of n, as the negative values are already included in the terms for positive n. However, the other person argues that this is incorrect and suggests using finite fourier, fourier, or laplace to resolve the problem.
  • #1
sommerfugl
2
0
Hello.

If I have this equation:

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And this general solution:

290zo5k.png


Would it then be wrong to write the above solution with only positive values of n? In my textbook they often write the result from a superposition with only positive values of n, becasue the negative values of n already are included in the terms obtained for positive values of n.
 
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  • #2
cos(-nkx)= cos(nkx) and sin(-nkx)= -sin(nkx) so all of the terms with n negative can be changed to n positive.
 
  • #3
HallsofIvy said:
cos(-nkx)= cos(nkx) and sin(-nkx)= -sin(nkx) so all of the terms with n negative can be changed to n positive.

This is wrong.. either use finite fourier, fourier, laplace. and resolve.. you should not get n=-infiinity... this problem should be so tough...
 

FAQ: Can the Wave Equation Solution Use Only Positive Values of n?

What is the wave equation?

The wave equation is a mathematical formula that describes the propagation of waves in a medium. It is commonly used in physics and engineering to model various types of waves, such as sound waves, electromagnetic waves, and water waves.

What is superposition in the context of the wave equation?

Superposition is the principle that states that when two or more waves overlap, the resulting wave is the sum of the individual waves. This means that the displacement or amplitude of the resulting wave at any point is the algebraic sum of the displacements or amplitudes of the individual waves at that point.

How is the wave equation used in real-world applications?

The wave equation has many practical applications in various fields. For example, it is used in telecommunications to model the propagation of radio waves and in seismology to study earthquakes. It is also used in medical imaging techniques such as ultrasound and MRI, and in engineering to design structures that can withstand seismic waves.

What are the variables in the wave equation?

The variables in the wave equation depend on the type of wave being modeled, but they typically include parameters such as time, position, wavelength, amplitude, and velocity. Depending on the specific problem being solved, other variables may also be included.

What are the limitations of the wave equation?

The wave equation is based on certain assumptions and simplifications, so it may not accurately describe all types of waves or situations. For example, it does not take into account factors such as energy loss and dispersion. Additionally, it is a linear equation, so it cannot accurately model nonlinear phenomena such as shock waves.

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