Question: A string is stretched along the x-axis, fixed at each end, and then set into vibration. It is shown in physics that the displacement y = y(x,t) of the point of the string at location x at time t satisfies the one-dimensional wave equation d²y/dt² = a² (d²y/dx²) where the constant a depends on the density and tension of the string. Show that the following functions satisfy the one-dimensional wave equation: (a) y = sin(x+at); (b) y = cos3h[x-at]); (c) y = sinkxcoskat (k is constant)