Practice Introduction - 11.3 | 11. One-Dimensional Wave Equation | Mathematics - iii (Differential Calculus) - Vol 2
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

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

11.3 - Introduction

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.

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What does the wave equation model?

💡 Hint: Think of examples of waves.

Question 2

Easy

What is the standard form of the wave equation?

💡 Hint: Recall the variables involved.

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 standard form of the one-dimensional wave equation?

  • $$\\frac{\\partial^2 u}{\\partial t^2} = c^2 \\frac{\\partial^2 u}{\\partial x^2}$$
  • $$\\frac{\\partial u}{\\partial t} = c \\frac{\\partial^2 u}{\\partial x^2}$$
  • $$u = c^2 t^2 + x^2$$

💡 Hint: Look for the equation that involves second derivatives.

Question 2

True or False: The wave equation can only be applied to sound waves.

  • True
  • False

💡 Hint: Consider other examples of wave phenomena.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given a vibrating string fixed at both ends, write the general solution using Fourier series. Consider the fixed conditions at $u(0,t)=0$ and $u(L,t)=0$.

💡 Hint: Think about how to incorporate boundary conditions into the Fourier expansion.

Question 2

Solve the one-dimensional wave equation with initial conditions $u(x,0) = sin(x)$ and $u_t(x,0) = 0$ on the interval $[0,\pi]$ with Dirichlet conditions.

💡 Hint: Remember to apply the boundary conditions to derive the specific solution.

Challenge and get performance evaluation