A circular loop of string rotates about its axis on a frictionless horizontal plane at a uniform rate so that the tangential speed of any particle of the string is υ. If a small transverse disturbance is produced at a point of the loop, with what speed (relative to the string) will this disturbance travel on the string?

Question

Philoid · Accepted Answer

υ

We need to calculate the tension to find the velocity of the wave. The tension will be due to the centrifugal force of motion.

The force for a small potion in the ring is given by,

Resolving the components and adding symmetric forces on the other end is given by,

But whole of this process was for half of the ring. I.e.

Now the velocity will be,

Hence the speed of the disturbance will be v.