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)//x_(0)]`
(c ) `1//(x + vt)`

Explanation

The converse is not true. An obvious requirement for an acceptable function for a travelling wave is that it should be finite everywhere and at all times. Only function (c ) satisfies this condition, the remaining functions cannot possibly represent a travelling wave.