You hold one end of a string that is attached to a wall by its other end. The string has a linear mass density of \(0.067 \mathrm{~kg} / \mathrm{m}\). You raise your end briskly at \(12 \mathrm{~m} / \mathrm{s}\) for \(0.016 \mathrm{~s}\), creating a transverse wave that moves at \(31 \mathrm{~m} / \mathrm{s}\).

(a) How much work did you do on the string? What are the wave's 

(b) energy, 

(c) potential energy, 

(d) kinetic energy?