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 -vt ` or ` x + vt `, i.e., `y = f( x+- v t )`. Is the converse true ? Examine if the following function for y can possibly represent a travelling wave `:`
(a) ` (x - vt ) 2`
(b) ` log[ ( x+ vt ) //x_(0)]`
(c ) ` 1//(x+vt )`

Answer 1

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