Wave Equation

Use Solve PDE to solve the wave equation.

$\blacktriangleright$ Solve PDE

${\dfrac{{\partial ^{2}y}}{{\partial t^{2}}}}$ = a2${\dfrac{{\partial ^{2}y}}{{\partial
x^{2}}}}$, Exact solution is : y$\left(\vphantom{ t,x}\right.$t, x$\left.\vphantom{ t,x}\right)$ = F1$\left(\vphantom{ -x-at}\right.$ - x - at$\left.\vphantom{ -x-at}\right)$ + F2$\left(\vphantom{ x-at}\right.$x - at$\left.\vphantom{ x-at}\right)$


\begin{example}
Let $y(x,t)$\ denote a vertical displacement of a vibrating str...
...\ (in red), $y(0.01,x)$\ (in
blue), and $y(0.02,x)$\ (in green).
\end{example}

$\blacktriangleright$ Plot 2D + Rectangular y(0, x)

The following surface shows the changing shape of the string as time varies from 0 to 1.

$\blacktriangleright$ Plot 3D + Rectangular y(t, x)