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Consider the three-dimensional wave equation. Determine the response to a unit point

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems | 5th Edition | ISBN: 9780321797056 | Authors: Richard Haberman ISBN: 9780321797056 284

Solution for problem 11.2.14 Chapter 11.2

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems | 5th Edition

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Applied Partial Differential Equations with Fourier Series and Boundary Value Problems | 5th Edition | ISBN: 9780321797056 | Authors: Richard Haberman

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems | 5th Edition

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Problem 11.2.14

Consider the three-dimensional wave equation. Determine the response to a unit point source moving at the constant velocity v: Q(x, t) = (x vt).(b) u(x, 0) = f(x) and u t (x, 0) = 0. [Hint: Use (11.2.24).] (c) Solve part (b) in the following manner. Let v(x, t) = tu(x, t), where u(x, t) satisfies part (a). [Hint: Show that v(x, t) satisfies the wave equation with v(x, 0) = g(x) and v t (x, 0) = 0.]

Step-by-Step Solution:
Step 1 of 3

a u 1 /"[*l = x{'.-:(.x /_(x ); 4x= -rlr 4" (a = l{t L-\ - g 4 n 4 \grt-rfQJus'*it t,*.z,) o( "l^t-+ CLLcrsL\b,,\* ,c] u_[ , d, -NC.;,,) I {"f*l---...

Step 2 of 3

Chapter 11.2, Problem 11.2.14 is Solved
Step 3 of 3

Textbook: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems
Edition: 5
Author: Richard Haberman
ISBN: 9780321797056

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Consider the three-dimensional wave equation. Determine the response to a unit point

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