You have learnt that a travelling wave in a dimension is represented by a funcation `y = f(x,t)` where `x` and `t` must appear in the combination `x-vt` or `x + vt`, i.e `y = f(x+- upsilon t)`. Is the coverse true? (Examine if the following funcations for `y` can possibly represent a travelling wave :
(a) `(x - vt)^(2)`
(b) `log [(x + v)//x_(0)]`
(c) `1//(x + v)`

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.