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

Answer

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 funcation © satisfies this condition, the remaining funcations cannot possibly represent a travelling wave.