Problem 4 A thin, flexible, unstretchable loop of string has mass per length . It is set spinning with angular frequency 2 in a gravitationless vacuum in such a way that it forms a stable circle of radius R. (a) [20 points] Find the tension in the string. (b) [20 points] Now suppose the string is given a small tap so that infinitesimal vibrations travel along the loop in the plane of the string in both directions. Compute the speeds of those waves relative to a non-rotating coordinate system.