PrepZii

formula

General Wave Equation and Direction

The source gives the one-dimensional wave equation and the direction associated with each sign.

\frac{\partial^2 y}{\partial t^2}=v^2\frac{\partial^2 y}{\partial x^2}

y(x,t)=f\left(t\pm\frac{x}{v}\right)

f\left(t+\frac{x}{v}\right)\text{ represents a wave travelling in the negative x-axis}

f\left(t-\frac{x}{v}\right)\text{ represents a wave travelling in the positive x-axis}