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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe37ebe49-731c-47f9-a49b-3a5f656faaa2%2F8261562b-fa8b-4abb-bb42-c1c6eb4e5f7a%2F7vi04u5_processed.png&w=3840&q=75)
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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