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) $(x + v t)^{2}$
(b) $log [(x + v t) / x_{o}]$
(c) 1/(x+vt)

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Solution

No, the converse is not true. The basic requirements for a wave function to represent a travelling wave is that for all values of $x$ and $t$ , wave function must have finite value.
Out of the given functions for $y$ , no one satisfies this condition. Therefore, none can represent a travelling wave.

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No, the converse is not true. The basic requirements for a wave function to represent a travelling wave is that for all values of x and t, wave function must have finite value.Out of the given functions for y, no one satisfies this condition. Therefore, none can represent a travelling wave.