Centrifugal waves on a flexible chain

A chain is attached at one end to a rigid rotating hub. Centrifugal force induces a nonuniform tension in the chain, which therefore supports transverse vibrations. Solution of the appropriate wave equation shows that the natural frequencies depend only on the rotational speed and the length of the chain relative to the hub diameter. Experiments demonstrating the existence of these vibrations show that an initial impulsive disturbance reoccurs as an “echo” in which all the eigenmodes reinforce each other. This echo occurs even though the eigenfrequencies are not harmonically related. The explanation of the echo is found in the (almost) linear relation between eigenfrequency and mode number.