How Does D'alembert Solution Work in Wave Equations?

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Discussion Overview

The discussion revolves around understanding the D'Alembert solution for wave equations, specifically how to apply it to a given example. Participants are seeking clarification on the method and its application, including the handling of integrals within the solution.

Discussion Character

  • Exploratory, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the D'Alembert solution and requests assistance with an example.
  • Another participant provides the specific equation related to the D'Alembert solution and inquires whether the user is expected to derive it or already has it.
  • A participant questions whether the integral in the equation can be simplified to a constant, indicating uncertainty about the next steps in the solution process.
  • Another reply suggests considering the integral of zero over a range, implying a potential simplification but does not clarify its relevance to the original problem.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants expressing differing levels of understanding and uncertainty about the application of the D'Alembert solution and the treatment of the integral.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the integral and the specific conditions under which the D'Alembert solution is applied. The participants do not clarify the dependencies or the context of the variables involved.

Who May Find This Useful

This discussion may be useful for students or individuals seeking to understand the D'Alembert solution in wave equations, particularly those looking for examples and clarification on mathematical steps involved in the process.

Niall101
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Hi I have been trying to figure out how this method works.

Searched the forum but got no results. Have attached an example I am trying to do. If someone could show me it would be great.

Or even show me a similar example worked out.

Thanks in advance
 

Attachments

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Do you have this equation to work with:

[tex]u(x,t)=\frac{f(x-ct)+f(x+ct)}{2}+\frac 1 {2c}\int_{x-ct}^{x+ct}v_0(s)\,ds[/tex]

to work with or are you expected to derive it?
 
Yes I have this equation. Does the integral go to a constant. ITs after this i don't know what to do
 
Niall101 said:
Yes I have this equation. Does the integral go to a constant. ITs after this i don't know what to do

Think about this:

[tex]\int_a^b 0\ dt = c|_a^b = c - c = 0[/tex]
 

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