Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
Graphing solutions to PDEs at various times
Reply to thread
Message
[QUOTE="sxal96, post: 5461621, member: 573469"] [h2]Homework Statement [/h2] Graph snapshots of the solution in the [I]x-u [/I]plane for various times [I]t[/I] if \begin{align*} f(x) = \begin{cases} & 3, \text{if } -4 \leq x \leq 0 \\ & 2, \text{if } 4 \leq x \leq 8 \\ & 0, \text{otherwise} \end{cases} \end{align*} [h2]Homework Equations[/h2] Assuming that c=1 and g(x) = 0, D'Alembert's solution for this question is $$f(x) = \frac{1}{2} \left(f(x+ct) - f(x-ct)\right)$$ [h2]The Attempt at a Solution[/h2] I'm struggling with this problem in its entirety. I don't understand how to graph the solution and why it's a rectangular box that is basically reversal of what seems to make sense when plugging in various values for x based off of the equation's characteristics. Conceptually, I realize that it is an infinite string and there's shifting of two waves that will overlap for some points. What I don't understand is how to go about drawing these graphs by hand. I confirmed with a classmate that the 'endpoints' for t are t = 2, t = 4, t = 4, and t = 6, based on the fact that t = distance/velocity. Please explain this to me like I'm 5. I tried Googling the concept to death and came short, and my professor and the textbook aren't particularly helpful. Any guidance would be very much appreciated. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
Graphing solutions to PDEs at various times
Back
Top