Practice Derivation of the One-Dimensional Wave Equation - 17.2 | 17. Modelling – Vibrating String, Wave Equation | Mathematics (Civil Engineering -1)
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Practice Questions

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Question 1

Easy

What does transverse displacement refer to?

💡 Hint: Think about how strings move when plucked.

Question 2

Easy

Write the wave equation derived from the force analysis.

💡 Hint: Recall the relation between acceleration and displacement.

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Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the equation for the wave speed (c)?

  • c = √(T/ρ)
  • c = T/√(ρ)
  • c = ρ/T

💡 Hint: Think about the properties of both tension and mass per unit length.

Question 2

The wave equation is a differential equation of which order?

  • True
  • False

💡 Hint: Consider the number of derivatives with respect to time and space.

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Challenge Problems

Push your limits with challenges.

Question 1

Consider a string with mass density ρ = 0.01 kg/m and tension T = 10 N. Calculate the wave speed c and discuss its significance.

💡 Hint: Be sure to plug the values into the wave speed formula correctly.

Question 2

If the tension in the string is doubled while keeping the mass density constant, how does the wave speed change?

💡 Hint: Think about the relationship expressed in the wave speed formula.

Challenge and get performance evaluation