Practice One-dimensional Wave Equation (11.2) - One-Dimensional Wave Equation

Practice: One-Dimensional Wave Equation

Lesson 11.2One-Dimensional Wave Equation

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9 questions

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2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the standard form of the one-dimensional wave equation?
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Recall the relationship between time and space derivatives.
Question 2.
What does the variable $c$ represent in the wave equation?
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Think about how fast the wave travels.
3Question 3.
What does $u(x, t)$ represent in the wave equation?
- Velocity
- Displacement
- Frequency
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Think about what the wave is doing at particular points.
4Question 4.
Is the one-dimensional wave equation applicable to sound and light waves?
- True
- False
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Consider the types of waves you encounter daily.
Question 5.
Solve the wave equation $\frac{\partial^{2}u}{\partial t^{2}} = \frac{\partial^{2}u}{\partial x^{2}}$ with fixed endpoints for initial conditions $u(x,0) = 0$ and $u_t(x,0) = 0$ .
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Consider how fixed endpoints affect the standing wave pattern.
Question 6.
Derive the wave equation in the context of a stretched string under tension, detailing each step.
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Think about the forces acting on a tiny piece of the string and how they relate.

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