|MLA Citation:||Bloomfield, Louis A. "Question 1573: Can pulling a superlong string send signals faster than the speed of light?"|
How Everything Works 24 Apr 2018. 24 Apr 2018 <http://howeverythingworks.org/print1.php?QNum=1573>.
Each portion of cable responds to being pulled by accelerating, moving, and consequently pulling on the portion of cable adjacent to it. There will be a long series of actions—pulling, accelerating, moving, and pulling again—that propagates your influence along the cable. A wave will travel along the cable, a wave consisting of a local reduction in the cable's density. It's a stretching wave. In that respect, the wave is a type of sound wave—a density fluctuation that propagates through a medium.
How quickly the density wave travels along the cable depends on how stiff the cable is and on its average mass density. The stiffer the cable, the more strongly each portion can influence its neighboring portions and the faster the density wave will travel. The greater the cable's mass density, the more inertia it has and the slower it respond to pulls, so the density wave will travel slower.
A cable made from a stiff, low-density material carries sound faster than a soft, high-density material. A steel cable should carry your wave at about 6100 meters/second (3.8 miles/second). But a diamond cable would reach 12000 meters/second (7.5 miles/second) because of its extreme stiffness and a beryllium cable would approach 13000 meters/second (8.0 miles/second) because of its extremely low mass density.
Regardless of which material you choose, you're clearly not going to be able to send any signals faster than the speed of light. It would take a density wave more than 100,000 years to travel the 5-light year length of your cable. And sadly, friction-like dissipation effects in the cable would turn the density wave's energy into thermal energy in a matter of seconds, so it would barely get started on its journey before vanishing into randomness.