Question
You have learnt that a travelling wave in one dimension is represented by a function $y=f(x, t)$ where $x$ and $t$ must appear in the combination $x-v t$ or $x+v t$, i.e. $y=f(x \pm v t)$. Is the converse true? Examine if the following functions for $y$ can possibly represent a travelling wave :
(a) $(x-v t)^2$$\quad$$\quad$(b) $\log \frac{(x+v t)}{x_0}$$\quad$$\quad$(c) $\frac{1}{(x+v t)}$
(a) $(x-v t)^2$$\quad$$\quad$(b) $\log \frac{(x+v t)}{x_0}$$\quad$$\quad$(c) $\frac{1}{(x+v t)}$