Calculating Rotation Angle: Mass & Cord Problem Explained

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so there's a blcok of mass 459 g attached to one end of a cord of mass 3.3 g and the other end of the cord is attached to a fixed point. The block rotates with constant angular spd in a circle on a horizontal frictionless table. Through what angle does the block rotate in the time that a transverse wave takes to travel along the string from the center of the circle to the block. I don't know how to start this at all.

EDIT: Nvm I got it
 
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I don't get it. I've tried using v = omega/r and v = sqrt(T/mu). I did calculate the radius to be .084 m at one point by substituting some equations and solving a cubic with r. I used T = (.45 kg + .0032kg*r)*(r*omega^2). I then combined that equation into the v = sqrt(T/mu) to get the value of r = .084. But I can't figure out where to go from there to get d(theta). I know omega = d(theta)/dt, but that's all I've got.