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 ± v t). Is the converse true? Examine if the following functions for y can possibly represent a travelling wave:
(a) (x – vt )2
(b) log [(x + vt)/x0]
(c) 1/(x + vt)
The converse is not true.
A wave function for a travelling wave is used to represent a travelling wave in the terms of x and t, wave function should also have finite value. Of the given alternatives, none can represent a wave function for a travelling wave.