0%) Consider the linear wave equation Utt = - o < x < ∞, t> 0, (2- where c > 0 is speed of the wave. Let G(n) be a suitably smooth function and let n = x + ct, - o < x < x, t> 0. Prove that G(x+ ct) is a solution of the equation (2.1).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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(20%) Consider the linear wave equation
Utt =
0 < x < ∞, t> 0,
(2.1)
where c> 0 is speed of the wave. Let G(n) be a suitably smooth function and let
n = x + ct,
x < ∞,
t > 0.
Prove that G(x+ ct) is a solution of the equation (2.1).
Transcribed Image Text:(20%) Consider the linear wave equation Utt = 0 < x < ∞, t> 0, (2.1) where c> 0 is speed of the wave. Let G(n) be a suitably smooth function and let n = x + ct, x < ∞, t > 0. Prove that G(x+ ct) is a solution of the equation (2.1).
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