Practice Modelling – Vibrating String, Wave Equation - 17 | 17. Modelling – Vibrating String, Wave Equation | Mathematics (Civil Engineering -1)
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Modelling – Vibrating String, Wave Equation

17 - Modelling – Vibrating String, Wave Equation

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the wave equation for a vibrating string?

💡 Hint: Think of how wave motion in strings is mathematically represented.

Question 2 Easy

List two assumptions made when modeling a vibrating string.

💡 Hint: Consider the physical constraints of the vibrating string.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the general form of the wave equation for a vibrating string?

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

💡 Hint: Recall the standard mathematical formulation for wave motion.

Question 2

True or False: The wave speed is inversely proportional to the tension in the string.

True
False

💡 Hint: Consider how increasing tension affects the wave speed.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider a string fixed at both ends, initially at rest. If displaced at the center and released, derive the equations governing its motion over time.

💡 Hint: What boundary conditions apply at the fixed ends?

Challenge 2 Hard

Suppose the string's tension is modified. Explain how this change impacts the wave speed and the normal modes.

💡 Hint: Think about how frequency relates to wave speed and string length.

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