This questions is about the wave equation in one dimension \frac{\partial^{2} \phi}{\partial x^{2}}=\frac{1}{c^{2}} \frac{\partial^{2} \phi}{\partial t^{2}} (a)Show that the wave equation becomes \frac{\partial^{2} \phi}{\partial \eta \partial \xi}=0 after changing coordinates

to n= x – ct and { = x + ct. (b) Find the most general solution to Eq. 1 by integration. (c) Using o as the ordinate and x as the abscissa, draw a picture of the o at t = 0 and att = 2 for initial conditions \begin{aligned} \phi(x, 0) &=\exp \left(-x^{2}\right) \\ \frac{\partial \phi}{\partial t}(x, 0) &=-2 c x \exp \left(-x^{2}\right) \end{aligned}