Practice Modelling – Vibrating String, Wave Equation (17) - Modelling – Vibrating String, Wave Equation

Practice: Modelling – Vibrating String, Wave Equation

Lesson 17Modelling – Vibrating String, Wave Equation

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8 questions

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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the wave equation for a vibrating string?
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Think of how wave motion in strings is mathematically represented.
Question 2.
List two assumptions made when modeling a vibrating string.
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Consider the physical constraints of the vibrating string.
3Question 3.
What is the general form of the wave equation for a vibrating string?
- $$ \\frac{\\partial^2 u}{\\partial t^2} = c^2 \\frac{\\partial^2 u}{\\partial x^2} $$
- $$ \\frac{\\partial u}{\\partial t} = c \\frac{\\partial^2 u}{\\partial x^2} $$
- $$ \\frac{\\partial^2 u}{\\partial x^2} = c^2 \\frac{\\partial^2 u}{\\partial t^2} $$
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Recall the standard mathematical formulation for wave motion.
4Question 4.
True or False: The wave speed is inversely proportional to the tension in the string.
- True
- False
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Consider how increasing tension affects the wave speed.
Question 5.
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.
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What boundary conditions apply at the fixed ends?
Question 6.
Suppose the string's tension is modified. Explain how this change impacts the wave speed and the normal modes.
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Think about how frequency relates to wave speed and string length.

4 more questions in this section. Enroll free to practise them all.