17.2 - Derivation of the One-Dimensional Wave Equation
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Practice Questions
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What does transverse displacement refer to?
💡 Hint: Think about how strings move when plucked.
Write the wave equation derived from the force analysis.
💡 Hint: Recall the relation between acceleration and displacement.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the equation for the wave speed (c)?
💡 Hint: Think about the properties of both tension and mass per unit length.
The wave equation is a differential equation of which order?
💡 Hint: Consider the number of derivatives with respect to time and space.
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Challenge Problems
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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.
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.
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