Practice Vibration of a String - 7.2 | Partial Differential Equations | Mathematics III (PDE, Probability & Statistics)
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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: Refer to the basics of wave propagation.

Question 2

Easy

Define what a node is in the context of standing waves.

💡 Hint: Think about where the string remains still.

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 does the wave equation for a string express?

  • A relationship between time and mass
  • The motion of strings over time and space
  • The tension in a string

💡 Hint: Think about how a string vibrates.

Question 2

True or False: A node in a standing wave is a point of maximum displacement.

  • True
  • False

💡 Hint: Consider where motion is minimized.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

A string of length 2 meters is fixed at both ends and under a tension of 50 N. Calculate the fundamental frequency of the string if its linear density is 0.01 kg/m.

💡 Hint: Remember to calculate the wave speed first using T and μ.

Question 2

Explain how the frequency changes if the tension in the string is doubled while keeping the length constant.

💡 Hint: Use the relationship between tension and wave speed.

Challenge and get performance evaluation