D'alembert solution Help (easy)

[Niall101]

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

 

[LCKurtz]

Do you have this equation to work with:

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

to work with or are you expected to derive it?

 

[Niall101]

Yes I have this equation. Does the integral go to a constant. ITs after this i don't know what to do

 

[LCKurtz]

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:

$$\int_a^b 0\ dt = c|_a^b = c - c = 0$$

 

[blue_raver22]

Hi there,

D'alembert solution is a mathematical method used to solve wave equations, specifically the linear wave equation. It involves breaking down the problem into simpler parts and using a change of variables to transform it into a standard form that can be easily solved. This method is commonly used in physics and engineering to solve problems involving waves, such as sound waves, electromagnetic waves, and water waves.

To understand how this method works, it is helpful to have a basic understanding of differential equations and Fourier series. D'alembert solution uses the Fourier transform to decompose the original wave equation into a series of simpler equations, which can then be solved separately and combined to find the solution to the original problem.

I recommend looking for online resources or textbooks that provide step-by-step examples of how to apply D'alembert solution to different types of wave equations. This will help you understand the process and how to use it for your specific problem.

I hope this helps! Let me know if you have any further questions. Best of luck with your problem-solving.