11.2 - One-Dimensional Wave Equation
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
What is the standard form of the one-dimensional wave equation?
💡 Hint: Recall the relationship between time and space derivatives.
What does the variable $c$ represent in the wave equation?
💡 Hint: Think about how fast the wave travels.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does $u(x, t)$ represent in the wave equation?
💡 Hint: Think about what the wave is doing at particular points.
Is the one-dimensional wave equation applicable to sound and light waves?
💡 Hint: Consider the types of waves you encounter daily.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Solve the wave equation $$\frac{\partial^{2}u}{\partial t^{2}} = \frac{\partial^{2}u}{\partial x^{2}}$$ with fixed endpoints for initial conditions $u(x,0) = 0$ and $u_t(x,0) = 0$.
💡 Hint: Consider how fixed endpoints affect the standing wave pattern.
Derive the wave equation in the context of a stretched string under tension, detailing each step.
💡 Hint: Think about the forces acting on a tiny piece of the string and how they relate.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.