A heavy box $($mass $80$ kg $)$ is connected to a big spool of rope $($a solid cylinder with radius $0\mathrm{.}45$ m and mass $90$ kg $)$ by a thin rope with a linear density of $0\mathrm{.}2$ kg$/$m $,$ as shown in $($Figure $1).$ The box is released from rest and allowed to fall. As the box falls, a wave travels up the rope from the box to the spool. What is the speed of that wave?