The x-component of (5) gives
where we have been careful to maintain the proper sign conventions on
the forces, with the right-hand direction regarded as positive, and
have used the fact that the segments do not move appreciably in the
x-direction (low amplitude approximation) and thus 
. Because we have been careful to use the version of
Newton's law which applies to finite-sized objects, the result
(6) applies to any segment. Thus, x and 
could be any two points along the string, the x-component of the
tension at any two points along the string are the same, and thus this
component of the tension is constant throughout. The horizontal force
which we apply to the end of the string
(Figure 1) sets the value of this constant. Thus, we
have as a general result
