A copper wire, whose cross$-$sectional area is $7\mathrm{.}80$ x $10^-6$ m$^2,$ has a linear density of $8\mathrm{.}53$ x $10^-3$ kg$/$m and is strung between two walls. At the ambient temperature, a transverse wave travels with a speed of $59\mathrm{.}3$ m$/$s on this wire. The coefficient of linear expansion for copper is $17$ x $10^-6($C$)^-1,$ and Young's modulus for copper is $1\mathrm{.}1$ x $10^11$ N$/$m$^2.$ What will be the speed of the wave when the temperature is lowered by $22\mathrm{.}7$ C$?$ Ignore any change in the linear density caused by the change in temperature.