A platinum wire (density 21.4 g/cm3) is 225 m in diameter and 0.450 m long. One end

Question:

A platinum wire (density 21.4 g/cm3) is 225 µm in diameter and 0.450 m long. One end of the wire is attached to the ceiling, while a 420-g mass is attached to the other end so that the wire hangs vertically under tension. If a vibrating tuning fork of just the right frequency is held next to the wire, the wire begins to vibrate as well.
(a) What tuning-fork frequencies will cause this to happen? You may assume that the bottom end of the wire (to which the mass is attached) is essentially stationary, and that the tension in the wire is essentially constant along its length.
(b) Justify the assumptions made in part (a).