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 $x+vt,$ i.e., $y=f(x\pm vt).$ Is the converse true? Examine if the following functions for y can possibly represent a travelling wave:
$\left(a\right)(x-vt{)}^2$
(b) $\log \left[\right(x+\vee y\left)/x_0\right]$
(c) $1/(x+vt)$

Answer 1

The converse is not true. For any function to represent a travelling wave, an obvious requirement is that the function should be finite at all times and finite everywhere.
Function a) and b) do not satisfy this requirement and hence cannot represent a travelling wave. Only function c) satisfies the condition.