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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 – υ t or x + v t, i.e. y = f (x ± υ t). Is the converse true? Examine if the following functions for y can possibly represent a travelling wave :(a) (x – υ t )² (b) log [(x + υ t)/x0] (c) 1/(x + υt)

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Solution

## The converse of the given condition is not true for the function. For a function to represents a travelling wave, the function should be finite at everywhere and at all times. (a) At x=0 and t=0, ( x−vt ) 2 =∞ So, it cannot represent a travelling wave. (b) At x=0 and t=0, log( x+vt x 0 )=log0 =∞ So, it cannot represent a travelling wave. (c) At x=0 and t=0, 1 x+vt = 1 0 =∞ So, it cannot represent a travelling wave. Thus, the given functions are not representing a travelling wave.

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