Describe the following waveforms in words (waveform, period, phase angle, direction & speed of travel … $etc$.). Demonstrate whether they are, or are not, solutions to the non-dispersive wave equation \[\frac{{{\partial }^{2}}}{\partial {{t}^{2}}}\psi (x,t)={{v}^{2}}\frac{{{\partial }^{2}}}{\partial {{x}^{2}}}\psi (x,t)\].

(a) $\psi \left( x,t \right)=4\cos \left( 4\pi x+3\pi t \right)-4\sin \left( 4\pi x+3\pi t \right)$

(b) $\psi \left( x,t \right)=3\cos \left( 2\pi x \right)\sin \left( \pi t \right)$

(c) $\psi \left( x,t \right)=3{{e}^{-\alpha x}}\cos \left( \frac{2\pi }{3}x-\pi t \right)$ , $\alpha$ is a constant