Practice Derivation of the One-Dimensional Wave Equation - 11.1.1 | 11. One-Dimensional Wave Equation | Mathematics - iii (Differential Calculus) - Vol 2
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the one-dimensional wave equation?

💡 Hint: Think about wave propagation in a medium.

Question 2

Easy

Name two types of waves described by the wave equation.

💡 Hint: Consider where you've encountered waves.

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?

  • ∂²u/∂t² = c²∂²u/∂x²
  • ∂u/∂t = c∂²u/∂x²
  • ∂²u/∂x² = 0

💡 Hint: This equation relates how wave displacement changes over time and position.

Question 2

True or False: The wave equation can only model sound waves.

  • True
  • False

💡 Hint: Think about different forms of wave propagation.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

A string with a length of 2m is under a tension of 100N and has a mass per unit length of 0.5 kg/m. What is the speed of a wave on this string?

💡 Hint: Focus on finding the values for T and μ to use in the formula.

Question 2

Describe how to modify the wave equation for a string with varying tension and mass per unit length along its length.

💡 Hint: Think about how each section of the string might behave differently due to changing properties.

Challenge and get performance evaluation