a) O Show that the wave equation Ytt = a²Yzz where a is a constant, can be reduced to the form Yuv = 0 by the change of variables u = x + at and v= x - at b) Use the results in part (a) and show that Y(x, t) can be written as Y(x, t) = (x + at) + (x-at), where and are arbitrary functions. Now, consider the wave equation in part (a) in an infinite one dimensional medium subject to initial conditions Y(x,0) = f(x), Y₁(x,0) = 0, -∞ 0. Using the form of the solution obtained in part (b), show that and must satisfy Jo(x) + y(x) = f(x), o'(x) - '(x) = 0.

a) O Show that the wave equation Ytt = a²Yzz where a is a constant, can be reduced to the form Yuv = 0 by the change of variables u = x + at and v= x - at b) Use the results in part (a) and show that Y(x, t) can be written as Y(x, t) = (x + at) + (x-at), where and are arbitrary functions. Now, consider the wave equation in part (a) in an infinite one dimensional medium subject to initial conditions Y(x,0) = f(x), Y₁(x,0) = 0, -∞ 0. Using the form of the solution obtained in part (b), show that and must satisfy Jo(x) + y(x) = f(x), o'(x) - '(x) = 0.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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