The wave equation W 0 = 10%
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
1=10
may be studied by separation of variables: u(x, t) = X(x)T(t).
If(x) = -k²X(x), what is the ODE obeyed by T(t)? []
Which of the following solutions obey the boundary conditions X(0) = 0 and X (L) = 0? [tick all that are correct
□sin() for & integer sin()
sin(
(2k+1)mz
2L
) for k integer
□ sin(2) sin() □ sin()
Which of the following is a possible solution of the above wave equation?
○ cos(kx)e-ket O cos(kex) sin(kt) ○ Az + B ○ 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%2Fd2eef452-b1c1-4df8-97fd-851738b3a553%2Fc2zv537_processed.png&w=3840&q=75)
Transcribed Image Text:The wave equation
1=10
may be studied by separation of variables: u(x, t) = X(x)T(t).
If(x) = -k²X(x), what is the ODE obeyed by T(t)? []
Which of the following solutions obey the boundary conditions X(0) = 0 and X (L) = 0? [tick all that are correct
□sin() for & integer sin()
sin(
(2k+1)mz
2L
) for k integer
□ sin(2) sin() □ sin()
Which of the following is a possible solution of the above wave equation?
○ cos(kx)e-ket O cos(kex) sin(kt) ○ Az + B ○ cos(kx) sin(kt) O None of the choices apply
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