A steel wire of length 0.50 m is stretched between two rigid clamps at a temperature at which it has exactly zero tension. It is then cooled…

A steel wire of length $0.50\ \mathrm{m}$ is stretched between two rigid clamps at a temperature at which it has exactly zero tension. It is then cooled uniformly by $\Delta T$ kelvin, and the clamps stay fixed so the wire becomes taut. For steel take Young's modulus $Y=2.0\times10^{11}\ \mathrm{N\,m^{-2}}$, coefficient of linear expansion $\alpha=1.2\times10^{-5}\ \mathrm{K^{-1}}$ and density $\rho=8000\ \mathrm{kg\,m^{-3}}$ (assume the wire's length, area and density are unchanged by the small strain). The fundamental frequency of transverse vibration of the wire is measured to be $60\ \mathrm{Hz}$. Find $\Delta T$ in kelvin.