You hold one end of a horizontal string and raise your hand during a time interval of \(0.18 \mathrm{~s}\), doing \(1.2 \mathrm{~J}\) of work on the string in the process. You then allow your hand to return to its original position. If the wave pulse you create travels along the string at \(67 \mathrm{~m} / \mathrm{s}\) and the linear mass density of the string is \(0.0282 \mathrm{~kg} / \mathrm{m}\), what was the vertical speed of your hand?