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MATH 286 Lecture Notes - Lecture 46: Wave Equation

United States

Intro to Differential Eq Plus

Mathematics

Dan Evans

University of Illinois

Discrete Structures

Data Structures

Introduction to Electronics

Analog Signal Processing

Probability with Engrg Applic

Computer Systems Engineering

Calculus II

Calculus III

University Physics: Mechanics

Introduction to Computing

Computer Systems & Programming

Wave Equation
Show that
<picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/952459547132328/question/0.webp?img=50d5928a633d0b85b1c397807e7ab6ff" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/952459547132328/question/0.png?img=d1ddf6e991b9ecbd4023a90eca3d9dbb" data-mlang="latex" data-equation="u%28x%2Ct%29%3D%5Cfrac%7B1%7D%7B2%7Dlbrack%7Bsin%28x-t%29%2Bsin%28x%2Bt%29%7Drbrack"></picture>
is a solution to the one-dimensional wave equation
<picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/952459547132328/question/1.webp?img=064fbcee28ed9ff347067edc3280628f" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/952459547132328/question/1.png?img=32fcbbb2306b0763cd808f93b0694311" data-mlang="latex" data-equation="%5Cfrac%7Bpartial%5E%7B2%7Du%7D%7Bpartialt%5E%7B2%7D%7D%3D%5Cfrac%7Bpartial%5E%7B2%7Du%7D%7Bpartialx%5E%7B2%7D%7D."></picture>

Wave Equation
In Exercises 99–102, show that the function satisfies the wave equation <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/769899572141133/question/0.webp?img=4d26ba0471c0c3dd5ef4cd077588cabc" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/769899572141133/question/0.png?img=46c9731ff53518689b5ca533473a9829" data-mlang="latex" data-equation="partial%5E%7B2%7Dz%2Fpartialt%5E%7B2%7D%3Dc%5E%7B2%7D%28partial%5E%7B2%7Dz%2Fpartialx%5E%7B2%7D%29."></picture>
<picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/769899572141133/question/1.webp?img=bbb0752ac91fe74786ef1b028c43d381" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/769899572141133/question/1.png?img=3c5113adbd8447c019d6eee02d280f44" data-mlang="latex" data-equation="z%3Dsin%28x-ct%29"></picture>

Wave Equation
In Exercises 99–102, show that the function satisfies the wave equation <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/291510765913517/question/0.webp?img=adc8c87fd904018da121feaf8a85b5aa" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/291510765913517/question/0.png?img=ef2a6d62c01a241ff7b6279738db1b5a" data-mlang="latex" data-equation="partial%5E%7B2%7Dz%2Fpartialt%5E%7B2%7D%3Dc%5E%7B2%7D%28partial%5E%7B2%7Dz%2Fpartialx%5E%7B2%7D%29."></picture>
<picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/291510765913517/question/1.webp?img=2e9c28eb602284c2321cb1647dd7fd53" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/291510765913517/question/1.png?img=16d8ae917186de86fa75e81fb5b6403e" data-mlang="latex" data-equation="z%3Dcos%284x%2B4ct%29"></picture>

MATH 286 Lecture Notes - Lecture 46: Wave Equation

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