A string that lies along the + x-axis has a free end at x = 0.
(a) By using steps similar to those used to derive Eq. (15.28), show that an incident raveling wave y1x, t) = Acos (kx+ wt) gives rise to a standing wave y(x, t) = 2Acos", tcoskx.
(b) Show that the standing wave has an antinode at its free end (x = 0).
(c) Find the maximum displacement, maximum speed, and maximum acceleration of the free end of the string.