1. a) Which of the following functions $u(x, t)$ are solutions for the 1D wave equation:
$\frac{\partial^2 u(x, t)}{\partial t^2} = v^2 \frac{\partial^2 u(x, t)}{\partial x^2}$
Where $v$ is just a constant (normally speed).
(i) $A(sin (kx-wt))$ where A is amplitude, k is wave number, w is angular velocity
(ii) $B \exp(x-vt)$
(iii) $(x+vt)^2$
(iv) $x^3 - v^3t^3$
(v) $x^2 - xvt + v^2t^2$