Wave Equation

Equation

• For a given string stretched along $x$-axis, the height at position $x$ at time $t$ is given by $u(x,y)$
• If it is disturbed, then it will vibrate according to the wave equation:

$$c^2\frac{{\partial }^{2}u}{\partial x^2}=\frac{{\partial }^{2}u}{\partial t^2}$$

With:

• Constant $c$ as the rate of vibrations, usually $c=1$

Solutions to Wave Equation

A solution will satisfy $u(x,t)=\sin (x)\sin (ct)$