A steel wire of length $1 \mathrm{~m}$, mass $0.1 \mathrm{~kg}$ and uniform area of cross section $10^{-6} \mathrm{~m}^2$ is rigidly fixed at both the ends without any tension. Its temperature is lowered by $20^{\circ} \mathrm{C}$ and transverse waves are set up by plucking the wire at the middle. The frequency of the fundamental mode is
$$
\left(\mathrm{Y}=200 \mathrm{GPa}, \alpha=1.21 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}\right)
$$