Solve the wave equation utt = uxx subject to boundary and initial conditions of the form u (0, t) = 0 ux (1, t) = 0 u (x, 0) = 0 ut (x, 0) = 1. This would describe a string that is attached to something on the left side, connected to a frictionless hoop/rail system on the right side, and suddenly hit from below in such a way as to impart a constant velocity to the string.

With the simplified model of the eye, what corrective lens (specified by focal length as measured in air) would be needed to enable a person underwater to focus an infinitely distant object? (be careful-the focal length of a lens underwater is not the same as in air! assume that the corrective lens has a refractive index of 1.62 and that the lens is used in eyeglasses, not goggles, so there is water on both sides of the lens. assume that the eyeglasses are 1.90