Stiffness is a linear phenomenon resulting from the finite diameter of the string.
Consider in place of the ideal string a bundle of ideal strings, such as a stranded cable. When the cable is bent, there is a restoring force arising from the net transverse component of axial string tension, as for the ideal string, but there is additionally a restoring force due to some of the fibers being compressed and others being stretched by the bending. The only restoring force in an ideal bar is due to stiffness. Setting gives solutions and . In the first case, the wave velocity becomes proportional to .