i. Show by direct substitution that u(x, t) = 1⁄2H(x − at) + ²H(x + at), where H is an arbitrary function, is a solution to the wave equation - a²uxx, aЄR, t≥0, -∞ < x <∞. Utt ii. Explain concisely how the initial displacement, u(x, 0), will evolve over time? You may include a plot if it helps your explanation.
i. Show by direct substitution that u(x, t) = 1⁄2H(x − at) + ²H(x + at), where H is an arbitrary function, is a solution to the wave equation - a²uxx, aЄR, t≥0, -∞ < x <∞. Utt ii. Explain concisely how the initial displacement, u(x, 0), will evolve over time? You may include a plot if it helps your explanation.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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