A guitar string is clamped at both ends. For the purpose of this problem we may consider it to have a length, L = x, and a wave speed, c = 1. Show that, u(x, t) = sin(x) cos(t) – } sin(3r) cos(3t) + sin(5x) cos(5t) (a) Satisfies both boundary conditions (clamped at both ends) (b) Is a solution to the wave equation (c) (Intermediate) Satisfies the initial condition if the guitar string is plucked - that is that (x,0) = 0
A guitar string is clamped at both ends. For the purpose of this problem we may consider it to have a length, L = x, and a wave speed, c = 1. Show that, u(x, t) = sin(x) cos(t) – } sin(3r) cos(3t) + sin(5x) cos(5t) (a) Satisfies both boundary conditions (clamped at both ends) (b) Is a solution to the wave equation (c) (Intermediate) Satisfies the initial condition if the guitar string is plucked - that is that (x,0) = 0
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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