Question

Q.4) A uniform string starched between the point x = 0, x = l is given the initial displacement y(x,0) = sin\frac{\pi x}{l}, 0 < x < l and initial velocity, \begin{equation} v(x) = \begin{cases} 0 & 0 < x < \frac{l}{4} \\ a & \frac{l}{4} < x < \frac{3l}{4} \\ 0 & \frac{3l}{4} < x < l \end{cases} \end{equation} Find the subsequent displacement.

          Q.4) A uniform string starched between the point x = 0, x = l is given the initial displacement y(x,0) = sin\frac{\pi x}{l}, 0 < x < l and initial velocity,
\begin{equation*}
v(x) = \begin{cases}
0 & 0 < x < \frac{l}{4} \\
a & \frac{l}{4} < x < \frac{3l}{4} \\
0 & \frac{3l}{4} < x < l
\end{cases}
\end{equation*}
Find the subsequent displacement.

Q.4) A uniform string starched between the point x = 0, x = l is given the initial displacement y(x,0) = sin(πx)/(l), 0 < x < l and initial velocity,

v(x) =
0 0 < x < (l)/(4)

a (l)/(4) < x < (3l)/(4)

0 (3l)/(4) < x < l

Find the subsequent displacement.

Added by Devin D.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Madhur L

02/15/2023

Step 1

Step 1: The wave equation is given by: $$ \frac{\partial^2 y}{\partial t^2} = c^2 \frac{\partial^2 y}{\partial x^2} $$ where c is the wave speed. Show more…

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Q.4) A uniform string starched between the point x = 0, x = l is given the initial displacement y(x,0) = sin $$ \frac{\pi x}{l} $$, 0 < x < l and initial velocity, $$ v(x) = \begin{cases} 0 & 0 < x < \frac{l}{4} \\ a & \frac{l}{4} < x < \frac{3l}{4} \\ 0 & \frac{3l}{4} < x < l \end{cases} $$ Find the subsequent displacement.