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The wave equation = may be studied by separation of variables: u(x, t) = X(x)T(t). If(x) = -k² X(x), what is the ODE obeyed by T(t)? [] ᎴᎢ Which of the following solutions obey the boundary conditions X(0) = 0 and X (L) = 0? [tick all that are correct-points will be deducted for wr answers] □ sin() for k integer □ sin(3) (2k+1) mz. 2L □ sin(- for k integer □sin(2) □ sin() sin() Which of the following is a possible solution of the above wave equation? ○ cos(kx)e-ket ○ cos(kex) sin(kt) O Ax+ B O cos(kx) sin(kt) O None of the choices apply

The wave equation = may be studied by separation of variables: u(x, t) = X(x)T(t). If(x) = -k² X(x), what is the ODE obeyed by T(t)? [] ᎴᎢ Which of the following solutions obey the boundary conditions X(0) = 0 and X (L) = 0? [tick all that are correct-points will be deducted for wr answers] □ sin() for k integer □ sin(3) (2k+1) mz. 2L □ sin(- for k integer □sin(2) □ sin() sin() Which of the following is a possible solution of the above wave equation? ○ cos(kx)e-ket ○ cos(kex) sin(kt) O Ax+ B O cos(kx) sin(kt) O None of the choices apply

Algebra & Trigonometry with Analytic Geometry
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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The wave equation 0² = 100 may be studied by separation of variables: u(x, t) = X(r)T(t). If(x) = -k² X(x), what is the ODE obeyed by T(t)? [] T. Which of the following solutions obey the boundary conditions X(0) = 0 and (L) = 0? [tick all that are correct-points will be deducted for wr answers] sin() for k integer □ sin(¹2) □ sin((2+1)*) for k integer □ sin(2) □ sin(7) sin() Which of the following is a possible solution of the above wave equation? ○ cos(kx)e-ket cos(kex) sin(kt) O Ax + B O cos(kx) sin(kt) O None of the choices apply
Transcribed Image Text:The wave equation 0² = 100 may be studied by separation of variables: u(x, t) = X(r)T(t). If(x) = -k² X(x), what is the ODE obeyed by T(t)? [] T. Which of the following solutions obey the boundary conditions X(0) = 0 and (L) = 0? [tick all that are correct-points will be deducted for wr answers] sin() for k integer □ sin(¹2) □ sin((2+1)*) for k integer □ sin(2) □ sin(7) sin() Which of the following is a possible solution of the above wave equation? ○ cos(kx)e-ket cos(kex) sin(kt) O Ax + B O cos(kx) sin(kt) O None of the choices apply
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