# Question Wave Equation Show that $u(x, t)=\frac{1}{2}[f(x-c t)+f(x+c t)]$ is a solution to the one-dimensional wave equation $\frac{\partial^{2} u}{\partial t^{2}}=c^{2} \frac{\partial^{2} u}{\partial x^{2}} .$ (This equation describes the small transverse vibration of an elastic string such as those on certain musical instruments.)

$u(x, t)=\frac{1}{2}[f(x-c t)+f(x+c t)]$
is a solution to the one-dimensional wave equation   $\frac{\partial^{2} u}{\partial t^{2}}=c^{2} \frac{\partial^{2} u}{\partial x^{2}} .$
Transcribed Image Text: Wave Equation Show that $u(x, t)=\frac{1}{2}[f(x-c t)+f(x+c t)]$ is a solution to the one-dimensional wave equation $\frac{\partial^{2} u}{\partial t^{2}}=c^{2} \frac{\partial^{2} u}{\partial x^{2}} .$ (This equation describes the small transverse vibration of an elastic string such as those on certain musical instruments.)
Transcribed Image Text: Wave Equation Show that $u(x, t)=\frac{1}{2}[f(x-c t)+f(x+c t)]$ is a solution to the one-dimensional wave equation $\frac{\partial^{2} u}{\partial t^{2}}=c^{2} \frac{\partial^{2} u}{\partial x^{2}} .$ (This equation describes the small transverse vibration of an elastic string such as those on certain musical instruments.)