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

1.	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)
Answer» SOLUTION :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.