When a string can be stretched by forces applied at its ends it is called an elastic string.

The natural length of an elastic string is its unstretched length.

Two forces, one at each end, must be applied to an elastic string in order to stretch it. You may argue that pulling one end will cause stretching if the other end is tied to a fixed object such as a wall, but remember that a force acts on the string at the point of attachment, e.g. where it is fastened to the wall.

Clearly the stretching forces must each act outwards; they must also be equal and opposite as otherwise the string would move in position and not just stretch.

An elastic string that has been stretched is taut; when it is in a straight line and is of natural length, it is described as `just taut'.

The difference between the stretched length and the natural length is called the extension and is often denoted by x.

We know that a taut string exerts an inward pull at each end and, by considering the equilibrium at one end of the string, we see that the tension is equal and opposite to the stretching force there.