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)

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.