You are testing a mountain climbing rope that has a linear mass density of $0\mathrm{.}0650$ kg$/$mkg$/$m$.$ The rope is held horizontal and is under a tension of $8\mathrm{.}00102$N$8\mathrm{.}00102$N to simulate the stress of supporting a mountain climber's weight. What is the speed of transverse waves on this rope? $$

You oscillate one end of the rope up and down in SHM with frequency $25\mathrm{.}0$ HzHz and amplitude $5\mathrm{.}00$ mmmm $.$ What is the wavelength of the resulting waves on the rope? $$

At tt $=0$ the end you are oscillating is at its maximum positive displacement and is instantaneously at rest. Write an equation for the displacement as a function of time at a point $2\mathrm{.}50$ mm from that end. Assume that no wave bounces back from the other end. $$

Express your answer in millimeters in terms of tt$.$