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Exercise 1 Consider the initial condition where f is the graph of an isosceles triangle over the interval 0≤x≤L and g(x)= 0. Using D'Alembert's formula sketch the graph of the solution of the wave equation at times -0, 31 4c¹ Hint: Derive the formula for f(z), extend to a function for all 4 ER as in the lecture and then remember that the graph of f(z- ct) is the graph of f(x) shifted to the right by ct and f(z+ct). is the graph of f(x) shifted to the left by ct.

Exercise 1 Consider the initial condition where f is the graph of an isosceles triangle over the interval 0≤x≤L and g(x)= 0. Using D'Alembert's formula sketch the graph of the solution of the wave equation at times -0, 31 4c¹ Hint: Derive the formula for f(z), extend to a function for all 4 ER as in the lecture and then remember that the graph of f(z- ct) is the graph of f(x) shifted to the right by ct and f(z+ct). is the graph of f(x) shifted to the left by ct.

Advanced Engineering Mathematics
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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Exercise 1 Consider the initial condition where f is the graph of an isosceles triangle over the interval 0<<L and g(z) = 0. Using D'Alembert's formula sketch the graph of the solution of the wave equation at times t = 0, 16 201 dc: Hint: Derive the formula for f(1), extend to a function for all 4 e R as in the lecture and then remember that the graph of f(z – ct) is the graph of f(x) shifted to the right by ct and f(r + ct) is the graph of f(r) shifted to the left by ct. L 3L
Transcribed Image Text:Exercise 1 Consider the initial condition where f is the graph of an isosceles triangle over the interval 0<<L and g(z) = 0. Using D'Alembert's formula sketch the graph of the solution of the wave equation at times t = 0, 16 201 dc: Hint: Derive the formula for f(1), extend to a function for all 4 e R as in the lecture and then remember that the graph of f(z – ct) is the graph of f(x) shifted to the right by ct and f(r + ct) is the graph of f(r) shifted to the left by ct. L 3L
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