The Singing Sign on Cuba Street

A shop sign of mass $M = 60.0\ \text{kg}$ hangs below a small ring. The ring is held up by two identical steel wire ropes whose upper ends are fixed to two brackets at the same height, one on each side; each rope makes an angle $\theta = 35.0^\circ$ with the vertical. Each rope has length $\ell = 2.00\ \text{m}$ between bracket and ring, diameter $D = 6.0\ \text{mm}$ and mass per unit length $\mu = 0.140\ \text{kg m}^{-1}$. For transverse waves, the bracket and the ring both act as fixed ends. Ignore the sag of the ropes under their own weight. When wind of speed $u$ blows across a rope, vortices peel off alternately from either side at frequency $f_{\text{s}} = 0.20\,u/D$; the rope 'sings' loudly when $f_{\text{s}}$ matches one of its natural frequencies.