Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 13.4, Problem 2E
To determine
To solve: The wave equation under given conditions.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
3. Solve the one-dimensional wave equation subject to the following conditions:
[v(0,1)= 0, v(7,t)= 0
Lv(x,0)=0,
= sin x
|t=0
10.7: Problem 7
Find the derivative of the vector function
r(t) = ta x (b + tc), where
(-3, —4, —2), b %3 (-2, —5, 4), аnd c %3D (-3, — 2, 4).
r'(t) = (O0-0>
a =
Show that the function
a(z, t) = bi sin )cos() + b sin cos( 2)
Tct
2nct
bị sin
COS
L
+ b2 sin
L
COS
L
where c, L, b1, b2 are nonzero constants with L > 0 and c > 0, is a solution to the
one-dimensional wave equation
c2.
Chapter 13 Solutions
Advanced Engineering Mathematics
Ch. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10E
Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Prob. 16ECh. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Prob. 28ECh. 13.1 - Prob. 30ECh. 13.1 - Prob. 31ECh. 13.1 - Prob. 32ECh. 13.2 - Prob. 1ECh. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Prob. 7ECh. 13.4 - Prob. 1ECh. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - Prob. 7ECh. 13.4 - Prob. 8ECh. 13.4 - Prob. 9ECh. 13.4 - Prob. 10ECh. 13.4 - Prob. 11ECh. 13.4 - Prob. 12ECh. 13.4 - Prob. 13ECh. 13.4 - Prob. 15ECh. 13.4 - Prob. 16ECh. 13.4 - Prob. 17ECh. 13.4 - Prob. 18ECh. 13.4 - Prob. 23ECh. 13.5 - Prob. 1ECh. 13.5 - Prob. 2ECh. 13.5 - Prob. 3ECh. 13.5 - Prob. 4ECh. 13.5 - Prob. 5ECh. 13.5 - Prob. 6ECh. 13.5 - Prob. 7ECh. 13.5 - Prob. 8ECh. 13.5 - Prob. 9ECh. 13.5 - Prob. 10ECh. 13.5 - Prob. 11ECh. 13.5 - Prob. 12ECh. 13.5 - Prob. 13ECh. 13.5 - Prob. 14ECh. 13.5 - Prob. 15ECh. 13.5 - Prob. 16ECh. 13.5 - Prob. 17ECh. 13.5 - Prob. 22ECh. 13.6 - Prob. 1ECh. 13.6 - Prob. 2ECh. 13.6 - Prob. 5ECh. 13.6 - Prob. 6ECh. 13.6 - Prob. 7ECh. 13.6 - Prob. 8ECh. 13.6 - Prob. 9ECh. 13.6 - Prob. 10ECh. 13.6 - Prob. 11ECh. 13.6 - Prob. 12ECh. 13.6 - Prob. 13ECh. 13.6 - Prob. 14ECh. 13.6 - Prob. 15ECh. 13.6 - Prob. 16ECh. 13.6 - Prob. 17ECh. 13.6 - Prob. 18ECh. 13.6 - Prob. 19ECh. 13.6 - Prob. 20ECh. 13.7 - Prob. 1ECh. 13.7 - Prob. 2ECh. 13.7 - Prob. 3ECh. 13.7 - Prob. 4ECh. 13.7 - Prob. 5ECh. 13.7 - Prob. 7ECh. 13.7 - Prob. 8ECh. 13.7 - Prob. 9ECh. 13.8 - Prob. 1ECh. 13.8 - Prob. 2ECh. 13.8 - Prob. 3ECh. 13.8 - Prob. 4ECh. 13 - Prob. 1CRCh. 13 - Prob. 3CRCh. 13 - Prob. 4CRCh. 13 - Prob. 5CRCh. 13 - Prob. 6CRCh. 13 - Prob. 7CRCh. 13 - Prob. 8CRCh. 13 - Prob. 9CRCh. 13 - Prob. 10CRCh. 13 - Prob. 11CRCh. 13 - Prob. 12CRCh. 13 - Prob. 13CRCh. 13 - Prob. 14CRCh. 13 - Prob. 15CRCh. 13 - Prob. 16CRCh. 13 - Prob. 17CRCh. 13 - Prob. 18CRCh. 13 - Prob. 19CRCh. 13 - Prob. 20CR
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Similar questions
- 5C. Under suitable assumptions derive one dimensional wave equation.arrow_forward7. Show that the equation f(x, y) = sin(x + y) + cos(x - y) satisfy the wave equation 0²1 01-01-1 dy² 0arrow_forward6. Simplified equations for an electric motor can be given O"(t) + 20'(t) = u(t) where 0(t) is the motor shaft angle, and u(t) is the voltage applied to the armature windings. a. Write down a state equation for the motor assuming a state vector x(t) = [0(t) O'(t)] and input u(t). b. Transform the state equation to that for a new state variable z(t) so that the new "A-matrix" is diagonal. c. Assuming that (0) = 0'(0) = 0, solve for x(t), t 2 0, when u(t) = e*, t 2 0.arrow_forward
- Q.4 Solve the wave equation: U, =U , +1+t-÷(1+e'), U (0,t) = U (7,1) = e' 2 U(x,0) = -, U,(x,0) = -arrow_forward(a) If V = x³ + axy², where a is a constant, show that +y = 3V əx ду Find the value of a if V is to satisfy the equation a²v__a²v = 0 ду? əx² (b) Show that wave equation is satisfied when a² = b²c² 1 a²u a²u Wave equestion: c² at² əx² u = cos at sin bx (c) Determine the first three non-zero terms of the Taylor series expansion for the given function. f (x) = e2× cos(x) about x =0 (d) The partial differential equation a²u a²u 3D 16 — х2 — 2у for 0 < x < 4, 0 < y< 2 (1.1) ax² ду? is subject to the boundary conditions u(x, 0) = 0 and u(x, 2) = 2(16 – x²) for 0arrow_forward3. Find the orthogonal trajectory of y =c cos xarrow_forwardThe 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 applyarrow_forward- 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) – v sin(0) and yu sin(0) + v cos(0).arrow_forwardWhich of the following is NOT a possible solution for Laplace's equation? (a) y = (AePx + Be-P*)(Ccos py + Dsin py) (b) y = (Acos px + Bsin px)(CEPY + De PY) (c) y = (Ax + B)(Cy + D) (d) y = (A P* + Be-P*)(CePy + Depy) O a O b O carrow_forwardChapter 13, Section 13.7, Question 031 Find parametric equations for the tangent line to the curve of intersection of the cylinders x +z = 25 and y + z = 10 at the point (4, –1,3). %3D O x(t) = 12 (t – 4), y (t) = -48 (t + 1), and z(t) = -16 (t – 3) O x(t) = 4, y(t) = -1+ 2t , and z(t) = 3 + 6t O x(t) = 4 + 12t , y(t) = -1 – 48t , and z(t) = -3+ 16t O x(t) = 4 + 3t , y(t) = -1 – 12t , and z(t) = 3 – 4t O x(t) = 4 + 8t , y(t) = -1, and z(t) = 3 + 6tarrow_forward2) What is the name of the following equation? a?u a?u ax?' ay? = f(x,y) a) Two-Dimensional Heat Equation b) Two-Dimensional Laplace Equation c) Two-Dimensional Wave Equation d) Two-Dimensional Poisson Equationarrow_forward5. Solve the following Wave Equation: a2U a2u 4 ax2 U(0, t) = U(r, t) = 0 and at2 au U(x,0) = 2sin x + sin 2x, (x, 0) = 0 0arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Intro to the Laplace Transform & Three Examples; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=KqokoYr_h1A;License: Standard YouTube License, CC-BY