(Eq. , consitutive relation) -
and to the slope of the string.
For a given shape of the string, we naturally expect the tension to be
in direct proportion to the tension applied to the string. The
basic reason for the proportionality to the slope of the string is
that the tension acts along the direction of the string and thus would
have no y-component when the string is perfectly flat and has zero
slope. Only when the string develops some slope ( 
) will the tension have a y-component. The greater the
slope, the greater the proportion of the tension in the y-direction.
Thus, we expect 
to be directly proportional also to 
.