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

11.3 - Introduction

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Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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Reference links

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