### Q.5:- 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:-**

No, the converse is not true. The basic requirements for a wave function to represent a travelling wave is that for all values of *x* and *t*, wave function must have finite value.

Out of the given functions for *y*, no one satisfies this condition. Therefore, none can represent a travelling wave.