Practice - Wave Equation and D'Alembert's Solution
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
Write the wave equation for one-dimensional wave movement.
💡 Hint: Remember, this is a second-order PDE.
What do the symbols $u$, $t$, and $x$ represent in the wave equation?
💡 Hint: Think about what each term relates to in a physical wave.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the wave equation describe?
💡 Hint: Think about phenomena like sound or light.
D'Alembert's solution involves how many arbitrary functions?
💡 Hint: Consider the components of the solution we discussed.
1 more question available
Challenge Problems
Push your limits with advanced challenges
A drum skin vibrates when struck. Using D'Alembert's solution, model the sound wave emitted from the drumhead assuming an initial shape: $$f(x) = \sin(\pi x)$$ and $$g(x) = 0$$.
💡 Hint: Use the right boundary conditions and understand how initial vibration generates the wave.
Consider a scenario where a wave is initially at rest, moving as two waves described by $$f(x) = e^{-x^2}$$ and $$g(x) = 0$$. Describe how this will look as time evolves.
💡 Hint: Focus on how the wave shape changes with time, but the height remains constant.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.