Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
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 related to the topic.
Question 1
Easy
What is the wave equation for a vibrating string?
💡 Hint: Think of how wave motion in strings is mathematically represented.
Question 2
Easy
List two assumptions made when modeling a vibrating string.
💡 Hint: Consider the physical constraints of the vibrating string.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the general form of the wave equation for a vibrating string?
- $$ \\frac{\\partial^2 u}{\\partial t^2} = c^2 \\frac{\\partial^2 u}{\\partial x^2} $$
- $$ \\frac{\\partial u}{\\partial t} = c \\frac{\\partial^2 u}{\\partial x^2} $$
- $$ \\frac{\\partial^2 u}{\\partial x^2} = c^2 \\frac{\\partial^2 u}{\\partial t^2} $$
💡 Hint: Recall the standard mathematical formulation for wave motion.
Question 2
True or False: The wave speed is inversely proportional to the tension in the string.
- True
- False
💡 Hint: Consider how increasing tension affects the wave speed.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a string fixed at both ends, initially at rest. If displaced at the center and released, derive the equations governing its motion over time.
💡 Hint: What boundary conditions apply at the fixed ends?
Question 2
Suppose the string's tension is modified. Explain how this change impacts the wave speed and the normal modes.
💡 Hint: Think about how frequency relates to wave speed and string length.
Challenge and get performance evaluation